I'm strapped for cash right now, but a game I'm about to run is going to have big fights with robots, and I'm thinking I'll need it. Any advice?

What system...? The reason I ask is because you could homebrew original rules that you can use to expediate encounters. I like the DeathWatch Horde Rules for mass combat. In Deathwatch each number of a horde represents how many their are. For example a mob of 30 on a magnitude of 30 would have roughly 30 hit points or wounds if you will. Each attack by the player{s} would effectively diminish the magnitude of the Horde. You could effectively generate mass combat in mechanics by converting weapons to do damage to the horde. For example melee combat would be half damage, magic, explosive or gun weapons would be full damage or you could even incorporate your own weapon damage by doubling the damage. The trick really is not maps or mechanics but the way one would write and role play the scene out. If there are several things happening at once, try describing in paragraph form including each of your players. Try seperating them in groups so that you have an idea and grasp of who is fighting who. For example I have nine players in my game with three seperate threads. I usually combat each one of them in turns but on a mass combat level I would seperate in the same post those that would take up various positions on the battlefield. In the end its really more work to map out a mass combat by making maps in my experience, even a small group of 6 game can get bogged down in mapping schemes. Try using your imagination and focus on mechanics and writing. These words of wisdom I think has developed my games so much more and I also couldnt take the credit without good players.

The thread tag says GURPS.

I assume he's talking about this: http://www.sjgames.com/gurps/books/masscombat/

I've not run it, but I've seen a lot of references in Pyramid and elsewhere; it seems very flexible and well-supported.

That said, do you need a detailed, semi-random resolution to resolve multiple battles, or are simple GM fiat with a few appropriate skill or attribute rolls sufficient for a singular event?

It depends. If the PC's did something like build one of the armies, or are the commander of an army, or something similar it gives you a reasonable system to adjudicate how much of a contribution they can make. On the other hand if the PC's are more like elite soldiers of one army I would instead determine how the battle will go if the PC's do nothing. Then give them some possible objectives (sabotage the death star, convince the mercenary leader to switch sides, invent a nuclear damper ect.) and determine how those actions would sway the battle.

Also note that this is a system mainly for resolving battles between armies. Dozens at least, IMO.

So maybe, it depends on your exact situation and what the PC's are doing exactly.

I cant comment on 4th ed as i dont have it,but ive worked with 3rd edition mass combat.
There are a lot of factors taken into account.

for example to your comparision. orcs would have a Troop strength. this is determined by the skill level of the troops and how many battles they have fought in,as well as just a racial number.

giants for instance have a higher TS (troop strength) and so for example a elite giant warrior going against 5 -10 green orks would wipe the floor with them.

like i said factors come into play! 1 is troop size (in your case this would be the horde magnitude! i have played deathwatch so i know what you are on about.)
If a horde is larger then its opposing force it gets given a bonus +. if its a racial enemy ,thats another +1,holding a position say a city is +8 and you add all these factors up giving you an overall Troop Strength to your army and theres.

heroes of 100-150pts carry bonuses too.as you can use them to do special events. like make a play to assassinate the enemy commander. and you allocate how much risk i think it is to the task.

you work out all these events, and their outcomes,troops vs troops determines a level of loss of troops and hence a victor.

Number of battles fought etc give you an over morale too.as well as your commanders leadership,strategy and something else ive gone mental blank on.

i have it and can try and help you work some out at least to how it was in 3rd. whether then you purchase 4th is up too you.