Turrets

[Seltin]

The ones you can't melee stand on to stop them shooting i.e. nameless ship.

Most of my guys barely do any damage since they have so much armor - whats the best way to handle them? Cassia uses her warp attack ability which does decent, and Pascal machine attacks do well, but my others guys barely do any damage.

[gimmethegepgun]

This is what Operative's Expose Weakness ability is for.

[Taifun_Vash]

Expose weakness and talents/abilities that reduce armor, power weapons.

[spammdc]

I use Cassia's ability to reduce will and toughness on them as well as her talent of reducing armor on "people" affected by her abilities.
Note: The above is also a great way to deal with daemons and just about any other bad guys and is a reason why I always have a person like Cassia in my group.