ME 3 Insanity Soldier Squad Reccomendations

It really doesn't matter a whole bunch about your losses in ME2. You won't eventually get Tali... but she's a late recruit in the game anyways. You have a much smaller squad base to select from in ME3 than ME2. Since you're missing Garrus (who's not the most useful anyways), basically, it's just James, Liara, and EDI... and Javik (if you get the From Ashes DLC). You'll re-acquire your ME1 Virmire survivor (Kaidan) about halfway through the game (if you make sure to do all the hospital visits, buy him an appropriate gift, and be nice to him... all so you don't wind up shooting him (and he is a powerful squad mate to have during the end game). You will be compelled to take Liara to Thessia and EDI to Chronos.

So, best squad out of the 4?... I'd personally run with Liara and James (who is a great tank with lots of firepower and inferno ammo).  Liara has warp ammo, so you can bring 3 different ammo types to bear on the enemy at one time.  If you're into biotic combos, then I'd go with Liara and Javik.  For a real all-renegade attitude, though, I think James and Javik are your best pair... but Javik does a pretty good job verbally beating up on Liara, so you can get that 2 on 1 feel.

Liara and Javik or Kaidan.  Just let the squad biotic combo everything.

As a Soldier you won't contribute all that much synergy with other squadmembers except maybe to detonate tech bursts or fire explosions with someone like EDI.  BE's are better since they have multipliers in their evolutions.

For your powers, Adrenaline Rush and Incendiary Ammo are the two best.  Incendiary DOT will interact with Warp DOT.