To my shame I haven't found myself any working strategy so far, so I have to rely on youtube. If I straight build I get owned from the first or second assault.
1v1 with insane is pretty tough for me. TvP with me terran I can only win by building 2-3 rax to block his exit and a bunker if he gets stalkers out. As soon as I have 5-6 rax pumping out marines I move into the base, usually there's a colossus waiting by then but not much else, 3v3,4v4 are way easier as long as you go for the resource points only(banshees/voids/mutas) and let your team(insane AI) handle the fight, but you have to be quick and preferably get the megaton map.
6-pool rush is also effective against terran but it's hit or miss, depending on your micro.
I like the coop games, but it's hard to find a good team to handle v hard, let alone insane, so I'm back to hard, where the lame rushes happen. I guess people are more concerned about their achievements than playing the game.
Hm I've never tried finding a random group to co-op with online. I can definitely imagine it being a crap shoot though. Hard enough to get decent players for team 3v3 or 4v4 play, lol.
For TvP, I'd suggest playing defensively until you have a sizeable army. As far as I can tell, early pushes are not a good idea b/c it's incredibly unlikely that your army will outsize the computer's army in the first like 10 minutes. I guess if you have good micro you could potentially out-play the AI. I usually wall-in (a bunker behind the depots can be helpful). Wall-ins might be necessary b/c it often rushes me with a lot of early zealots if I don't wall. Hold a xelnaga or leave an SCV outside of his base for vision, so you'll see when the push is coming.
You want to try and force engagements that are positionally favorable for you. The computer is pretty aggressive, so set up a good concave & draw it to you. Don't just "a-click" into his base; you'll get reamed. Or let it get choked on your ramp. I usually strictly defend (first my main ramp, then my expansion ramp/choke/whatev) for the first 2-3 pushes by the AI. Keep in mind that the AI won't harass you, so you don't have to be afraid of like, muta-harass or warp prism surprises.
But I bet harassment would work great against AIs, esp if you're engaging their army during the harass. I can't manage that many things at once, so I rarely harass.
Though BSing the AI can be pretty fun. When I need a quick break from work, I'll fire up the insane AI and cannon rush it The code they added to make the AI resist building pylon/forge in its base is not robust. Trying different things makes the AI do all sorts of hilarious shit.