ProBasketball News has an interesting list of some lower tier free agents that could be had for cheap. Old friends Gerald Green and Wally Szczerbiak make the list and I don't think they are very good fits here (Wally can still shoot, but that's about it). However, there are some interesting names of guys that I wouldn't mind seeing here for the right price (ie. very cheap).
Ike Diogu and Jason Collins would both be cheap big men and at the very least they'd work harder than Patrick O'Bryant did. Desmond Mason might cost a bit more than the other guys on this list, but he'd probably fit the role of backup small forward pretty well (if healthy). Then there's a collection of point guards on this list that I'm not terribly familiar with, including CJ Watson, Royal Ivey, and Ronnie Price.
I don't see anything linking any of these guys to the Celtics, but after the market has shaken out with the big names, they might be good options to look into.