However introduces a simple contradictory statement and can usually be substituted with but:
The blue ones taste good, however [but] the red ones do not.
Still introduces a contradictory statement in the face of contrary evidence and can usually be substituted with even so:
The same company makes the blue ones and the red ones from the same recipe, still, I don't like the red ones.
Note that in many cases one word can be exchanged for another in a sentence, but the resulting sentence may convey a slightly different meaning.
The blue ones taste good, still, the red ones do not.
This now means, that even though the blue ones taste good the red ones don't;
Still is often used when you are disagreeing with someone who has presented an argument for their position. You are essentially saying, Even given your arguments I still don't agree with you.
"You should come to the party. Joe will be there."
"Still," [you are considering the fact that Joe will be there] "I don't think I'll be going." [ You have decided against attending even though Joe will be there.]
In your example using however:
I enjoyed the trip, however my roommate did not.
you are simply stating two facts: you liked it, your roommate did not.
If you use still:
I enjoyed the trip, still, my roommate did not.
you are now saying, even though I liked it, my roommate did not.
You are now saying that your liking the trip could have had an influence on whether your roommate liked it too, but it didn't.