nasty cat fights wont stop

So heres the deal, I moved in with a friend of mine, his girl has an older (11yo or so) female cat, she is very territorial and hard to handle (even by humans), I to have an 11yo cat, he is very friendly, social and outgoing, he tired being friends with the female cat but she just wont let it happen, its been over 3 months now and all they do is fight, although sometimes its just my cat trying to come up to my room to visit me and the female cat sits at the top of the stairs always and thats where most of the fights start, Ive heard that a cat constantly sitting in one particular doorway is an aggresive pose, not too sure what to do about this but my room mate and his girl are gettin pissed being that her cat has no front claws and my cat has 7 claws on each paw, so yes, there is blood, now Im not saying hes perfect, he does get pissed at times and go after her but most of the time hes just minding his business and she gets the fighting started. BTW there is a dog (pitbull) in the house too, which both cats get along with just fine, not sure if that has any bearing on this or not. Any help would be greatly appreciated.
Thanks

In my experience, 3 months isn't really that long for cats to get to know each other. They might not ever like each other, but eventually they will be able to ignore each other and not fight. I have 2 cats (also a boy and a girl, with the girl being the less friendly cat) that didn't get along at first, and it took them at least 6 months to stop fighting, and close to 2 years to groom each other and be friends.

That said, there are some things that I think you can do to help. Find a toy that both cats like, and play with the friendly cat in front of the other one, then try to involve the other in the game too. I call it "play therapy". If they won't even tolerate that, then maybe try getting them used to being around each other by rewarding them with treats when they get close and don't fight.

I'm sure other people know of other ways, but I usually just use play and treats to try to get cats to like each other, and most of all, unfortunately you have to give it time.

Have you tried Feliway or Rescue Remedy?

I agree with the Rescue Remedy & the Feliway. I'd spot treat any area that they mark with their faces, furniture at cat nose level & the area where he's blocking. These 2 products made a huge difference around here... The 2 cats that were fighting are laying on the couch together across the room.