I'm not really the most knowledgable person on 'Nam, but I'll try to give some info...
The Army is, well, what you think of when you think the word "army". They're job is to work on the ground... although they also have their own aircraft to support them.
Aircav is just a division of the army; just like the 101st or the 82nd airborne are divisions of the army. I think there were a few different Aircav divisions, but I'm not certain. Anyway, I'm not exactly sure how their mission differed from the rest of the Army's mission, really, aside from flying in on helocopters... But regular Army and Marines flew into LZ's on helos as well, so again, I don't know what exactly Aircav was tasked with. I do know the unit in "We Were Soldiers" was aircav, but that doesn't really help.
Seals are the Navy's special forces. Their job is to do covert ops for the Navy, like clearing obstacles from enemy beaches, securing enemy boats, killing terrorists on oilrigs, yadda yadda. Again, I'm not really big on Nam history, so I couldn't tell you what the Seals did in Nam.
The Marines basically do the same thing as the Army (fight on the ground), only they do it better
. But seriously... historically, Marines were the guys on ships who would shoot rifles/muskets at the guys on the other ship, and who would also board the other ship for some hand-to-hand fighting. Later on Marines were used to do fighting on land, after being dropped off of their ships. In more modern times, the Marines have been used pretty much the same as the Army, only the Marines specialize in amphibious landings. Also, the Marines are the first ones into a hot country, because there are always "floats" of Marines sailing around the ocean, who can be deployed into a country in some 72 hours.
But like I said, the Marines are used for the same kinds of missions as the Army (not JUST amphibious landings). The Marines are technically a department of the Navy (the
men's department), but they are considered one of the branches of the military (Army, Navy, Airforce, Marine Corps, Coast Guard). The MC is smaller than the army (less than a third the size?), but is generally better trained, due to higher standards. In the Iraq war, there was basically a 2-pronged assault out of Kuwait: the Army drove through the desert kinda westward to Bagdad, while the Marines drove straight up the main freeway, fighting from town to town.
In Nam, the Marines were in charge of certain areas of the country, while the Army was in charge of other areas. I'm pretty sure that the battle of Ia Drang valley was fought by the Army, but there may have been some Marine activity in the region at different times. Oh yeah, the events in "We Were Soldiers" took place in a part of Ia Drang as well. Some famous battles fought by the Marines include the seige at Khe Sanh, the battle for ancient Hue city, and the landing at De'nang (not really a battle, but it was where the first US combat forces came to Vietnam).
I don't really know about the rest. I don't know what LRRP stands for, but my guess would be "Long Range Recon Patrol". No idea bout MFR though... SF I would think stands for "Special Forces", but I don't know WHICH special forces it refers to (Rangers? Seals? Marine Recon? PJ's? Delta Force (don't think it existed then...)? Green Berets?). Each of these special forces has different missions, and each of them is a part of one of the branches of the military (Rangers -> army, Seals -> Navy, etc). Green Berets are noteworthy though, as far as Nam goes. They would basically operate alone, and would be inserted into some village. There they would train local Vietnamese and conduct offensive/defensive operations against the Vietcong (North Vietnamese guerillas). The movie "Apocalypse Now" is about one of these guys.
There are about a million books on the Vietnam war out there, but I wouldn't know which ones to refer you to. I started reading a book called "Semper Fi Vietnam", which basically covers everything the Marines did in 'Nam, but I put it down now that school started.