Will Avulstein Gray-Mane follow you into other quests? Most wikis say he will, but I just don't see how. Do you go to the fort to free his brother and then leave? How is this done? And does he take up a spot as a follower?

Avulstein is just a "quest follower". He follows you only during the quest he is related to: http://www.uesp.net/wiki/Skyrim:Followers#Quest_Followers

You can actually use him in other quests, but to do that, you have to meet up with him at Northwatch Keep (so he joins your party), then leave. In other words, you must leave his quest undone. If you already have a follower with you, he (and his 2 mercs) will join in addition to that follower, but I'm not sure whether you can recruit another follower if Avulstein joins you first. He is essential, but the two guys with him are not.

On that very page it has a check mark for "usable in other quests"

Yes, this probably means that you can drag him everywhere once you've joined with him near Northwatch Keep. He will follow you wherever you go until you have freed his brother.

Avulstein will not prevent you gaining or dismissing normal followers, but his buddies can die while following him, and if they do, you may find attacking the keep much more difficult when you do decide to do it.

How funny this topic comes up...about 2 months ago, I tried to get Avulstein Gray-Mane to follow me into other quests (I looked up potential followers on the wiki and he interested me the most). I met him and his 2 friends near that fort and instead of entering the fort I tried to backtrack and head east. They all followed me and my follower for a quick 10 seconds but suddenly they reversed course and headed back to the spot near the fort.

So what gives? Am I doing something wrong? Did the OP figure it out? I also recall reading that section of the wiki that stated he'll follow you for other quests. I am on the Xbox 360. I decided to reload to a previous save....so basically Avulstein is still in Whiterun in my game...

You did nothing wrong; Avulstein is not a follower that's it. The wiki should be corrected.