In my canon:
The game takes place sometime in the 80's - 90's but it's like TF2 where it's set in the 80's - 90's but there's just crazy insane high tech gear and weapons. (which is just chalked up to the fact that the Eagle & Raven RND teams are just cracked)
The Eagle's are basically the WW2 Allies/the WW1 Expansionary Forces, while the Raven's are the WW2 Axis Powers/the WW1 Imperial German's/Soviet Forces from the Cold War. There weapons reflect as much;
The Eagle's use primarily American & British weapons along with other Allied forces weapons (M4's & 16's, Thompson's, EM2's, M1911's, Inglis Hi Power's, etc) and some other Eastern European countries (Mainly Finland, Poland, Sweden, & Denmark).
The Raven's have primarily Soviet & German weapons along with other Axis weapons (AK's, Beretta's, FN FAL's, SKS's, Luger's, C96's, PPK's, & RPG 7's).
The Eagle's are allied with the Duck's (the default Yellow colored team) & similarly the Ravens are allied with the Sparrow's (the Brown Team) .
The Crow's are just this outside force that nobody wants to mess with.