Get gas asap, defend with about 4 tightly packed sunkens at each exit.
Expand to the south and defend as you did in your main.
Gather up a large group of lings, hydras, and lurkers(maybe some hive units,too) and attack the protoss base. Aside from defending yourself, target the unit-producing buildings and probes.
As for the nuke itself, Mengsk's base is to your left and you can defend yourself accordingly(he's the only that uses nukes and tanks)
Once you've destroyed the protoss, the mission is essentially over. Take toss' resource nodes and go dev/muta/guard/scourge and go after the Dominion.
VS the UED, it's best to take the ground route. Having Devourers will definitely help, though. (some may get yamatoed, but you should have no problem replacing them)
Mass hydras with defilers(DS) and devourers maybe some lings and lurkers and the base should fall very quickly.
Note if your running low on resources, take Mengsk's.
Things to remember:
-Hotkey your hatcheries so that you're constantly producing.
-Take out the protoss BEFORE they psi-storm and maelstrom.
That maybe it unless someone else wants to contribute