I haven't met star gods yet, but numbers from wiki say that they're very nasty psionics, especially on higher difficulties. Coordinators have 90+rnd(56) attack strength, for example. On capped stats (60\40) your gal would have only 68 defence, so star gods can terrorize them gals without failure.
Of course, there are psi-defence boosting armours, but they're not absolute protection, sadly.
Assuming capped stats, ragnarok will increase defence to 102, ghost - to 90 (10 power + 2 from skill + 10 from outfit), bio suit - to 98, xeno - 103 (50 from bravery - 15 from loss of power). Other armors give much more minor defence bonuses to my knowledge.
From others' words, their ghost beams appear to ignore armor, forcing to rely on resists only. In that case, I'd prefer to use bio suit gals against them if possible, since: they take only 40% plasma damage, improve psi-defence (but gals are still vulnerable, take care) and regenerate health. Invisibility forces to rely mostly on aoe damage: explosives, flamethrowers etc.
I *may* try to tackle their ships or\and do a quick battle with them to see how much my tactics will work (or not), but I need to prepare.