I'm going on a self-appointed Starcraft: Brood War challenge - beat as many AI allied against you as possible using a non-Terran race (Terrans arguably have the easiest time doing so, with Siege Tanks decimating AI units and having overall the most cost-effective units with minimum micro (against the AI's simple attacks), on a "non-money" map (as in, not Big Game Hunters or similar map that lets you turtle in one base forever). Recently I defeated 5 AIs with both Protoss and Zerg:
It's not exactly the most representative of Starcraft experiences, as for both Protoss and Zerg the approach basically relies on blocking the choke point with buildings in such a way that the Protoss AI can't reach your Sunken Colonies with Zealots; Marines die to Sunken Colonies / Photon Cannons. (Terrans have the advantage of being able to lift off with their buildings, but with Zerg and Protoss, you are stuck inside your first base for quite a while without Shuttles or destroying your wall when necessary). Then, you tech to fast Dark Templars or Lurkers, send them to enemies post-haste, and your aim is to destroy their Command Centers / Nexi, and prevent peons from rebuilding. Your invisible units must take out 2-3 AIs at least; then, you get your late tech and finish off the map with Carriers or massive Zergling drops under Dark Swarm. You move out to expand by either just making mass cannons and taking out Tanks with your remaining Dark Templar, or in case of Zerg, by moving out with a massive Hydra / Lurker force.
In my 1v5 games I deliberately avoided letting the computer play Zerg because 1) if the Zerg AI goes early pool and rushes you with zerglings, it kinda breaks the challenge and 2) the Zerg AI had the tendency to "hang up" sometimes, stopping any development and offense past a certain minute mark, not expanding or doing anything at all. I decided to move up to 1v7, full random, and I actually underestimated the Zerg AI: it adds Overlords to its mass Hydra attacks, which makes them actually deadly to Lurkers and Sunkens alike, and the Zerg AI is also notoriously hard to destroy with Lurkers alone due to ubiquitous detection, unless I send a critical mass of Lurkers their way immediately (around 4-5, to one-shot any Hydras and decimate their Drones in one fell swoop; it's very unaffordable, as you can imagine). The best approach I can think of is to try and destroy Protoss and Terrans ASAP and turtle it out against the Zerg while destroying their mineral lines.