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Catholic Space Nazis - the Imperium of Man.
Empy - Because it's boring to write EMPEROR.
Emprah - how Indrick Boreale says it in Dawn of War: Soulstorm.
Also commonly called Emps and the Big E.
Spess Mehreens - Another one from Boreale, this time an affectionate nickname for space marines.
Pie Plate - The large ordnance template. Called a "Pizza" in Italy, for obvious reasons.
Smurfs - The (blue-and-white liveried) Ultramarines. Occasionally used for Space Marines in general (SMurfs).
Papa Smurf - Marneus Calgar, Chapter Master of the Ultrasmurfs.
Rowboat Girlyman - Roboute Guilliman, Primarch of the Ultramarines.
Blue Space Communists/Weeaboos - The Tau.
Weeaboo Space-Commies as well.
Also know as Commie-Fish because of their vehicle naming conventions.
Greys - Tau, because of their resemblance to the Roswell Greys
Bolter Bitches - Sisters of Battle. Alternate name for flamethrower-focused version: Flamer Bitches.
Nuns With Guns - see above
Toasters - Necrons
Space Elves, Elfdar - Eldar.
Among the less charitable (usually SMurf players), the nickname is often extended to Pansy Space Elves.
Space Puppies - Space Wolves
Also known as Space Yiffs or Space Furries.
T-shirt and Flashlight - The flak armor and lasgun of guardsmen.
Big Mac - Any melta, but especially multi-meltas. So named because a "multi-melta" sounds like some kind of delicious cheese sandwich.
'Nids - Tyranids.
Also sometimes applied to the Vajra from Macross Frontier, due to quite obvious similarities.
'Nids has actually become so widespread that its been adopted as an in-universe nickname, particularly in the Ciaphas Cain books.
Failaddon / Failbaddon - Abaddon thanks to losing all 13 Black Crusades and never making it past Cadia despite having an army of Space Marines, Daemons and Cults vastly outnumbering the Imperial Forces.
Tsundere-Sun/Sundere/ShadowTsundere - Commander Shadowsun.
Cap'n Gabe - Blood Ravens Brother Captain (later Chapter Master) Gabriel Angelos.
Space Marines, particularly the first edition models, are occasionally referred to as "Beakie Boyz" or "Beakies" due to the distinctive pointed "snout" of the Mk VI Corvus Armour's helmet (itself inspired by the medieval bascinet). Though few Space Marine models use the older helmet, the Orks still use "Beakie" as shorthand for Space Marine, and a certain image board asserts that the earlier Space Marines were much more macho and badass than the Nancy-boys in skull-faced helmets that run around today.
Many Orkish nicknames are popular among players as shorthand for various races and wargear: "Panzees" = Eldar; "Beakies" = Marines; "Umies" = Imperial Guard, regular humans; "Dakka" = guns, cannons; "Choppa" = close combat weapons; "Stunties" = Squats; "Fishies" = Tau
Life Support Toilet - the Emperor's Golden Throne, for the function it serves and the unfortunate implications of the word "throne."
Also known as the Golden Toilet or Golden Shithouse, for the same reasons mentioned above.
Musical Wounds - the tactic of exploiting 5th edition wound allocation rules.
Greenwing - regular Dark Angels soldiers, as opposed to the more elite black-armored Ravenwing and white-armored Deathwing.
More here -- with thanks for the ones copied.
Pimps in Space - Rogue Trader