I would note - that the official rules for how you set up the board would obligate you to have the 2' section be "your side" the to then use the 4' width as the 'sides' of the board - if that makes sense.
Per the rules pg. 92-93 obligate you to have 12" of space between your army and the mid point of the board. Thus, basically what you're lacking is lateral space - there should still be the normal 2 turns of shooting at the Orks before they get to you that you'd have on a 6x4 table.
At that point alone he probably shouldn't even have space to fit his army on the table in anything resembling order if there's any terrain on the table at all (and there should be)
Now, if you guys are playing with the 4' sections as your deployment zones and consequently are basically starting in assault range of each other it is *dramatically* favoring horde assault armies to a level that is close to unfair - because he has assault range on you in one turn.
My solution to these brawls would be as follows;
If you are setting up with 2 feet of distance between the starting armies, as is dictated by the rules, then the failure of your army is in not having functional shooting tools - quick math - 6x 30man Ork squads w. PK Nob and 1 KFF Big Mek translates as around a 1500 point army for your side.
1500 points ought to give you lots of options to inflict pain. I may want to see the list to critique it. (I'll also note, 1500 is kind of a silly big army for such a small table - you may want to suggest 1000 point games and watch as suddenly it's nowhere near as tough to weaken the horde before it gets to you)
Now, if you're starting with only...I dunno, maybe 12" between armies and are deploying in a 1x4 area that's pretty screwy, because, as I said, the Orks will get to assault Turn 1 and that's not fair to a shooting army. Still, we can try to work with that - here are my suggestions; because beating up Ork mobs with DE should be easy once you understand how easy it is to screw them up.
First off - try to get first turn (1 more round of shooting) if your deployment zone is 2x1 (as it should be) deploy towards the back edge of the table. If the deployment is 1x4 then deploy tightly in a corner (this will finctionally make all the Orks who - due to space - will need to be placed further away from you have to struggle to get at you because they'll have to travel further and will also have to try to get around all the Orks in front of them.
Units to consider
Beastmaster squad w. Baron Sathypants (3x Beastmasters, 4x Razorwing Flocks, 5x Khymarae) - +1 to initial starting role gives you first turn and likely one more turn of shooting - which is pretty important.
The beastmaster squad, as described, will give you 42 attacks at initiative 5-6, so, even if an Ork Mob assaults you you stand a decent chance of almost killing them even before they get to swing - and if you assault them you stand a decent chance of ending them outright.
The Beastmaster squad deploys in a line in front of your army (your army does not start all the way forward, but instead hugs the back edge of the board.
Behind the Beastmasters will be your shooting. Venoms and Razorwings w. Dissies and S.Cannons are your friends. Ravagers with Dissies aren't abd, but more Venoms and poison shooting are overall better (that said, even Ravagers with Lances aren't 'bad' if you're doing a TAC list, and I'll explain uses for them later) Also, Wracks with Liquifiers riding with Haems. Versus Orks, Wracks are probably a better option than Wyches for a couple of reasons, we'll get to that.
Your primary targets are the closest Orks to you - simple, yeah? Now - let's quickly consider that Beastmaster squad and what happens when Orks charge it;
You'll get 42 attacks
Baron will hit 2.6 and cause 1.33 wounds
Khymarae will hit 7.5 and cause 3.75 wounds
Beastmasters will hit 1.5 and cause .5 wounds
Razorwings Flocks will hit 10 and cause 3.33 (1.66 will be rending)
After saves (6+) the Orks will suffer 7.69 wounds or so. That's your average to be expected in practice you'll usually do a bit less or a bit more so expect 6-8 or so dead Orks and you'll rarely be disappointed by your performance.
What that tells you is - as long as the Ork Mob is down to around 10 boyz that you'll win the fight even if they assault you (3 Boyz and 1 Nob aren't going to do much - remember to put Nob wounds on Beastmasters or Khymarae if possible - or hope he bases Baron Sathypants and swings on the Shadowfield for lulz) So you'll cause more wounds and, with you initiative, will probably sweep the squad.
If you do that then your barricade holds and he has to try to get a *new* mob in to try to puncture your defenses.
So, when shooting your goal is to shoot up the closest mob until it's down to about 10 boyz (or maybe a bit less - if they fail a morale roll odds are they'll be insta destroyed since they will be unable to fall back through the Ork wall behind them - and that works out well for you) So don't waste shooting - weaken them up to the point they're going to have trouble puncturing your Beast skirmishers, but no more than that - waste no dead Orks!
With Razorwings, if you bring them, their initial shooting should go for big and thickly packed mobs of boyz (shouldn't be hard to find - but the point is you should usually be aiming for the middle of the army with your missiles) - an optimal shot is to aim for the mob that the KFF is in, because if you can drop that mob under 10 and force a morale check you can rob him of 2 Klaws at once and also of his KFF as well. After that initial missile drop then they can turn their shooting to the closest squads just like the rest of the army.
Also, random important thing to keep in mind - splinter weapons are AP 5, so Orks need cover or they don't get their 6+ save.
Okay, so now the Orks are getting really close...
Basically you'll have 1 totally free round of shooting and, then depending on how you guys use the table, you're looking at assault after that. So what can you do to weaken the situation? Now, you do have the Beasts out there, and they can absorb a small charge easily - or even opt to go aggressive and charge the Orks on your turn (depending on the situation this might be a good idea - it sort of depends on how big the mob is, how many mobs are left, and whether they'll be shooting you prior to doing their charge or not)
But you do have some other options - let's consider if you are bringing some Raiders/Ravagers w. Lances because your army isn't custom built to kill Ork horde (And doesn't need to be). What do you do with a flying weak vehicle that can probably only fry 1-3 Orks or so a turn? Useless, right? Oh, no, not at all - let's see this;
Here comes a bunch of Orks - whatever shall we do, they're going to hurt us!
The two lines above represent Ravagers/Raiders with Lances (with Dissies they're probably better off shooting, but you could still do this with Raiders and still shoot with them that round too)
But the basic gist is this, move your vehicles up 7-12" and put them broadside in front of the Orks.
Now the Orks can't assault you - because they have big floating walls in front of them. Being Orks, they'll assault the floating walls (Waaaagh, waaaalls!!!) This is great because, first off the walls will be hard to hurt (Boyz will needs 6 and 6 to glance them, and Nobz will need 6 to hit and 2+ to damage). Iff they explode the Raiders then the explosion will tear into a bunch of tightly packed Orks - hopefully killing a couple. If it's a Wreck then the Orks now have dangerous terraint o walk over (again, possibly killing more Orks) or will have to walk around it, slowing their advance.
Functionally this buys you ANOTHER TURN OF SHOOTING AT ORKS. You just magically made the board "bigger" because now it will take the Orks longer to get the assault they want - you also probably killed some more boyz, and every dead Orks is a win.
It's even better if they didn't kill the transport, because then you can fly away and do the same trick again, because - y'know - screw Orks.
Orks are in the line! We is doom-ed!
Despite the best laid plans of deldar and men - the Orks will eventually get to your line. In your example there are basically 200 Orks walking at you - that's a lot of Orks to kill, so how do we punish them even more for getting there?
This is where the Wracks and Haems come into play.
Fly up in your Venoms/Raiders and shoot them - but also start dropping down Liquifier templates. The templates ignore cover, ignore armor saves, and will wound Orks on 4+. Orks being Orks, you can probably get a lot of models under any given template - and if you have multiple liquifiers this could easily allow you to be killing 8+ Orks from a single Wrack attack.
Don't get out of your vehicles though - make the Orks work at swinging on a 4+ to hit and then trying to smash through flickerfields or whatnot.
You don't get out voluntarily because of two reasons.
First, if the Orks fail to kill the vehicle they'll be packed tightly around it - excellent, drop out more liquifiers and keep frying them apart.
If they do wreck the vehicle then the Wracks will deal with explosions easier than the Orks (FNP is good) and then the Wracks can Liquify them and charge the Orks (and Str 3 Orks do *not* want to fight T4 + FNP Wracks, let me assure you)
So let's put it together;
Deploy in a corner and/or back against the board edge.
This will make the Orks walk maximum time to get into assault with you.
Also, Ork mobz in front will keep Ork mobz in back from getting stuck in as they kind of traffic jam trying to wedge in at your position.
Focus fire on closest Ork mobz - make them weak enough that your defensive line can win in assault with them. Force the Orks to burn a full assault phase fighting your roadblock - that's an extra turn of shooting you get.
Use lance vehicles as moving roadblocks when the Orks get too close - sacrifice them for the greater good and laugh as Orks die in explosions or fail to get off assaults because they're having to walk around moving terrain.
When the Orks get closer use Liquifiers on them - force Orks to hit vehicles that have moved, counter assault once you're forced out of vehicles.
Taking all my suggestions there are lots of alternate options you can consider.
A Grot wall is a possible solution instead of Beastmasters (a Wych wall is as well - though smart Orks would just shoot it)
Liquifiers are very good (Shredders are good too - but are useless against pretty much everything else - so it's a question of if you're custom building)
You will want a lot of splinter cannons - lots of splinter cannons are good versus lots of armies. But the primary goal is to get a lot of shooting that can shoot 36+ inches so that you cna shoot them Turn 1, and then just retreat as he gets closer and keep shooting him every turn - don't sweat trying to get s.rifles into range until the Orks get up in your face anyway.
Wyches can work pretty well if you don't like Wracks - they're still solid Ork killing machines.
Hope some of that is useful to you.