I'll go one at a time here, though I think I only have 4 of 5. Still gotta grab the 5th.
Shrink Ray:
Okay so, this game did come quite useful for me. Playing on Supernova and wanting my companions to deal more ludicrous damage, I can focus fire on a strong enemy and have them melted in seconds, to which all the weaker foes around are quickly disposed of. I find this gun quite fun and enjoyable, but only under certain circumstances, not a daily use weapon.
Prismatic Hammer:
I'm a bit mixed by this one because I can not fully see the effects when fighting. I do enjoy the varying damage types it produces, but how combat works in this game, to be honest that makes this hammer quite horrible. Up until science 100 where you can constantly upgrade this without doubling the cost to ludicrous levels of bits (unless you exploit for unlimited bits). Though bits are not too difficulty to come by. I haven't found any differences to any weapons whatsoever. The only thing that matters is how much damage it does outright or the DPS. Nothing else matters, literally. I am saying this by having less than 20 offense skill abilities. For instance, skill 8 in long guns yet I can snipe a lot of enemies easily and do ludicrous amounts of damage flat.
This hammer at least adds variety and is fun to use for two-handed. I really like it, but combat is worthless in the game.
Mandibular Rearranger:
Okay, so this one did help out on certain occasions because it has the odd "freeze enemy" ability. This is valuable as this means you can focus fire and melt any enemy that is frozen, or use TTD to focus fire another enemy as you wale on the frozen enemy until death. Imagine fighting the last boss and this effect happens. You literally reduced the final boss to be utterly useless until you finish it off while your companions can cover you and melt all the useless enemies around.
Gloop Gun:
I just got this one, but had a little play with it. I say, best used indoors and crowded groups. This gun has a chance to render multiple enemies hit by it to float (it's AoE), rendering less enemies dealing damage to you and companions, increasing your survivability as well as your companions. When playing on Supernova, this is quite nice not needing to spam heal to keep alive. In open areas, however, this is not a weapon of choice.
EDIT:
Mind Control Ray:
I just got this gun yesterday, been a while since I last started up the game. I B-lined for this after finishing up almost all of Monarch. I didn't have time to test in an actual fight, so I slaughtered Fallbrook with it. It was amazing to be able to get anyone dangerous to stop shooting at me and fight his own allies. Since the town was actually weak, relative to me, the mind control ray actually killed them quicker to be useful. I could imagine using this on tankier enemies would be better. Too bad I killed off possibly all the most deadly enemies on Monarch, on accident mind you. If you wanted 'OP', then take this gun and have fun.
Note: I have 100 Science, and 1 (of two) perks giving me 50% increased Science weapon damage. Turned level 21 and have 2 flaws, so perks were easier to obtain. Now I am a drug addicted captain afraid of heights... Wait, this sounds bad.
In general, anything that will cause enemies to not hurt you is good. The majority of the science weapons do just that. It's a good way to quickly pick off enemies as your companions do all the DPS for you. If you solo though, best to leave these weapons alone. They won't meet up to the standard of a solo-sniper who can kill anything in one hit no matter the difficulty. With maybe anything with 3k health or higher being the exception.