I've taken in many strays at this point, but I'll just mention the 3 that are living with me right now, since they all reacted differently.
Dusty was 4 months old when we found him, no adjustment period at all. He even used a makeshift oatmeal-in-cardboard-box litterbox perfectly (before we got a chance to go to a pet store). He wasn't interested in his new surroundings at all, he kept climbing back up into my lap when I tried to make him explore! After he was fixed, he's turned into the best cat I've ever met.
Bobby was a little harder--he's 2 years old and while he would come to people outside for food, he's still getting the hang of being a "pet". He was very shy, hid under the bed alot, and there were very small confrontations with him and Dusty, but they never escalated beyond hissing and growling. After only a few days, they were playing together and grooming each other. Dusty taught him how to play with toys and how to use his voice. Two months later, he's just now beginning to really warm up to me, he'll jump up in bed just looking for attention and just yesterday gave his first AUDIBLE purrfest and rolled onto his back for me!
Kuro just joined us a week ago. He's having a harder time adjusting. He loves me and my fiancee, loves to be pet and held, but only when the other cats aren't around. He's very upset around them and growls alot. He's slowly making his way into our bedroom because it smells so heavily (to him) of the other cats. He's making slow but sure progress, but we've been putting "Good Cat" calming solution in his drinking water to try to mellow him out towards the other cats. He meows at the door to the apartment alot. He would win the gold medal for litter box "effort"--he furiously tries to cover his messes but ends up dragging his claws along the plastic and the wall so hard that little spirals are left in their wake. He has had a few accidents, but for the most part, he uses the litter box. Dusty, the trooper that he is, has taken it upon himself to clean up after the other two in the litter box--if he smells anything, he tries to cover it for them.