I won't try to name which brands are which, but I'll take a crack at describing the difference between groups.
Group I is "basic" refined oil. Mostly used now in cheap-to-make oils like 10W30, though even those have some oil from the next group to meet API quality requirements.
Group II is hydrocracked oil. Given more refining for higher quality, more uniform characteristics, fewer impurities. Most non-synthetic oils have a hefty dose of this stuff.
Group III is severely hydrocracked oil. As above, but more so. Because of the large amount of processing required to make these, they can be officially marketed as "synthetic". Many flamewars as to whether this is deserved or not.
Group IV is "true" synthetic oil. Rather than taking oil out of the ground and trying to clean it up enough to be usable in an engine, this is basically manufactured from scratch to ensure there are no impurities. Very uniform.
Group V is everything else. Esters and other chemicals that have useful purposes in making oil, but don't really fall into any above category.
It can be hard to define strictly where one group ends and another begins, so there are ranges in the groups too. For example, group II+ is an oil in between II and III. A product can contain oil from several different groups too, so you could hear "Oil X is group III/V" meaning it has some of both groups in it.
I'm sure I'll be deservedly flamed for getting some detail wrong. I think I deserve a medal for writing this on a board with no edit button.
(Yes, I know the work-around.)
