Every time I've tried to roll to escape enemy fire, I end up getting shot and killed.  It's pretty much always a better idea for me to just try to swing away from the enemy.  Am I doing something wrong, or does the roll really not do much to help you?

I don't use it personally. Once I finally discovered it was in there I couldn't understand what circumstance I'd use it in.

Grrrr.....

Maybe it's more of a single player thing.

It can help avoid a sniper shot if you time it right and are approaching rather straight forward and blatantly, but mostly its not used for much else.

I find that the roll is useful in one main respect. First of all, it temporarily increases your movement speed (in that you speed up while you're rolling). However, the downside to this is the second or so of immobility that follows the roll. Thus, I don't use the roll in combat, I only use it when i'm trying to pick up lots of health packs really quick. If there's health packs in a line and i'm being chased, i just roll into them and pick up all of them rather than lumber towards them at a walking pace

I used it once on a blind date. Very useful.

I enjoy punching clowns.

I used it at some point, like the levels where the snipers are. But in my opinion the roll is not very effective, the roll distance is so short, and as soon as you hit roll you cant do it again straight away, there is a little recovery time on the animation. So i did not  find it super useful.

you only really need the evasive roll when you fight groeder because it is the only way to dodge him when he turns all electric and charges towards you

No, the combat roll is useless for anything except making you move slower.. I've been sniped to death while midroll in single player, in multiplayer it's useless against anything with a fire rate (I don't even try to roll from shotguns) and the screen-shake plus controller rumble while rolling makes it distracting to use.

Stay in the air, its impossible for enemies to hit you in midair on the normal difficulty of single player, and swing is almost always the best thing to do in multi unless you're camping with a machine gun or something from within a fortified position.