The soldiers you encounter throughout most of the game are simply mutated/enhanced humans.... When you're driving around in your buggy, if you stop by the petrol station and go across the road, hop over the broken fence and walk behind the large gas tank, you'll see a spray-painted history of the mutations... it goes from monkey to human to the foot-soldiers you're up against. The soldiers have implants and other "enhancements."
Also, when you're in the jail with Alyx, you'll see a few things on the monitors: namely, some poor frankenstein-ish bastard with bolts sticking out of his head. You see one of these guys again on your pod ride when you're in the citadel.
According to the Prima strategy guide (I hate that they put some background into the guide that ISN'T in the game... bastards... fortunately, people have posted stuff on various forums), the slug-looking thing you see on the monitors in Breen's office is a "Combine Advisor." And, apparently, the Combine are creatures that roughly fit the description of that liason thingy. You can also noclip around the map any time you see that thing on the mointors and view the entire model for yourself (all videos in the game take place in hidden rooms somewhere in the map and are just projected, like a GUICam in D3).
As far as who the Combine are and why they're interested in earth:
The outset of the ressonance cascade in the first Half Life... that temporal rift caught the attention of the Combine... a race that tends to invade other planets, use them up, using the native population(s) as fodder and labor, and move on... Think of it like a mixture between the Borg from Star Trek and the overall theme of Independence Day with a dash of Matrix here and there.
Anyhoo, this site is pretty good at going over the whole saga. It's a timeline of the whole story, and, according to the HL2 fanatics, it's useful for piecing stuff together.