HM, I think a guy like Kevin Mueller or Kevin Millar would be good value signings. Both are 34 years old, right handed (Millar switch) with .360 or higher OBPs. Mueller can play 3rd, 2nd, 1st and DH. Millar can play 1st, OF, DH. So if you sign one of those guys there is some roster flexibility. If you have one of them as a full time DH, I'd expect them to possibly put up close to 20HR's given that they have time to study tapes between at bats etc. But the biggest selling point for either guy is that you can probably have them cheap. Other teams may stray away because of age, but these 2 guys seem to me to be the types of players Oakland pick up. It's no Willy Mo but I think that they could be servicable.
All in all, realistically I don't think they will sign anyone. This lineup looks very good to me when healthy: