The Fithik in Devil's Den were saying immune when I was using my Cryo shotgun. I need to go back there to finish off some quests, so I'll test it out again then.
EMP : Linkers are Weak and it damages both their health & armor.
Fire : Forean Machina are Immune, Kael are Immune, Treebacks/Treemites/Treelurkers are all Weak.
Ice : Forean Machina are Immune, Fithik are Immune, Kael are Weak, Thrax Infantry are Weak (Fire as well, as listed), Magmonix are Weak.
Electrical : Hominus Machnia are Immune (also sonic, as listed).
Virulent : Caretakers are Immune, Xanx are Immune, Hunters are Weak (However all non-machines can be delt more damage by Virulent damage type when they have low or no armor reserves, and are very resistant to it with high armor reserves).
I belive Miasmas are weak to fire, and immune to sonic - but I am not 100% on either. I'll check when I have time.
Im unsure of what damage type Reconstructor Bots reflect, although I am certian I remember they reflected something in Beta (which may not apply now).
Also, Reconstructor bots & Warden bots are both immune to something alike, but I also dont remember that one either.
FYI (and I've bugged this in-game) the Hunters are still showing up as immune to electric in Pools and in the instances in Pools. Their immunity was supposed to change to sonic in 1.4.
Flaregashers are immune to Fire
Treebacks are immune to physical
Mox are immune to electric
Everything without armor is weak against virulent
Basic guidelines
Physical does average damage against most things and the ammo is generally cheaper (except rockets)
Laser does better damage than physical but there are more things that are immune to it the ammo costs more than physical
Electric does better damage than laser with even more things immune to it with mid range ammo costs
Fire does better damage than electric with fewer things immune to it but the ammo costs much more
Ice does less damage than fire or electric but hurts almost everything ammo costs are the same as fire
Virulent damages health but not armor
EMP damages armor but not health
All Hominus Machina are not immune to sonic, as the table indicates. Sonic is strong against Hominus Machina, noticably better than EMP (at least in Palisades and below, where I've had a chance to verify it).
Some key "Strong against X" constants aren't listed.
Virulent is strong against Atta.
Cryo is strong against Kael.
Incindiary is very strong against Beam Mantas.
Forean Machina are immune to both Fire and Ice and weak to EMP and.
Warnets are immune to Electric and weak to Virulent
Mox are immune to Electric (someone already said) and weak to Virulent.
Reconstructor-bots are immune to EMP (some at least if not all) but still weak to Sonic.
Boregar are immune to Fire and Weak to Virulent.
Lightbenders are Immune to Laser and Weak to Virulent (low health).
Lashers are Strong against Ice (maybe immune, i forget) and weak to Fire and Virulent.
The general rule is fairly simple: Most Wildlife are Strong or Immune against the damage type that they use.
EG: Flaregashers which hurl fireballs at you are immune to fire damage. Howlers who use he sonic cone attack are immune to Sonic. Mox and Warnets who zap you all the time are immune to Electric. Note that this doesn't always mean immunity, it can simply mean high resistance.
The opposite is also usually true. If wildlife uses a damage type they are weak to the opposite. Opposites are Fire-Ice, Electric-Physical, EMP-Virulent, Sonic-Laser.
EG, Flargashers are Fire immune but Weak to Cold. Warnets are Electric immune but weak to Physical.
Almost all Thrax are weak to Fire.
Almost all machines are weak to EMP and Sonic and Strong to Physical and Ice.
Almost all Wildlife are weak to Virulent.
These are only "guidelines" though. Sometimes these generalities conflict (ie: Atta and Ticks are Wildlife but both use Virulent damage so one or the other may be true). DG have sometimes mixed things up though.
EG, there's a lot of places where ReconstructorBots and WardenBots are together which means you can romp through with EMP damage on the face of it. To put some difficulty back in the equation they gave ReconstructorBots EMP immunity to stop it being a brain-dead situation.
The last one is that certain mobs have been given Immunity for no apparent reason. For instance Boregar are immune to Fire damage (so how that guy is gunna use em to make Bacon I have no idea). This doesn't make sense until you look at mob mixing. Boregar are very often found fighting Mobs that are weak to Fire (Treelurkers). If caught in the "this weapon is best against X" crossfire you are stuck holding a Fire weapon to kill Treelurkers and being attacked by Immune Boregar.
The only one I have yet to figure out is Xanx. They are immune to virulent and it appears just to be an arbitrary decision made only to annoy the crap out of people using Decay (well, that's the biggest effect it has on me anyway).
Thrax have also been given arbitrary immunities (although according to Lore they make more sense). Thrax are easy to kill but there's Physical, Sonic, Laser, Electric and Virulent Immunity. This covers all of the cheaper ammo types which I don't think is coincidence. I think it was done to force you to make the decision to rotate weaponry or go expensive and use Canister weapons for broad-spectrum effectiveness.
Also keep in mind that Weakness is relative. A mob may have Fire Resistance but no Physical Resistance. Because Fire weapons deal more damage than Physical you might kill something faster with Fire than Physical even though some damage is resisted and the same goes for coloured weapons (this is one of my main dislikes about the combat system in TR).