I often buy/find things for people too so they'll like me, I know just what you're talking about there.

I don't know about the other people in the office; tell me, have they worked there longer? I joined an office of 6 women and they had all been there before and had some friends and interests from before I came so I was left out for a few years until I was there long enough to "fit in". I can sort of understand that, that they might want to see an old friend for a lunch hour. Was a bit cruel/pointed how they told you "about" it and asked you to eat somewhere else though. I would have given you warning a couple days earlier if that were the case, that it was a special friend and we wanted to talk about old times and it would probably bore you, etc.

It seems hard for you not having anything in common with the two teams though. I was in another engineering firm and was the 2nd oldest person there but they'd all graduated from the same school and were all mostly young so I didn't fit there because I was from a different school.

I would try not to take it quite so personally, they may not see what they are doing or some of them may see and just be "cruel" like children? I would see if there weren't some "nicer" people in the groups I could become "better" acquainted with and/or participate in some of their conversations as well as I could? It's hard when you are feeling a bit paranoid and like it could be something you are doing. Maybe trying to invite yourself makes you look too "needy". What interests and hobbies do you have outside work? Do you have any friends outside work? Two years does seem like it would be a long enough time for them to start including you in things.