We are over the cap and have used all available (non-Vet-min) exceptions. When Bynum is waived (since no one is taking on his full salary, he will pass through waivers) he will be UFA and will be eligible to sign with anyone for the vet minimum or any team using their existing cap space.
Amnesty is a different thing. It goes in 3 tiers, basically. Once a player is waived by anmesty, he goes into a modified waiver process. Teams have the ability to make the following bids:
1) Full claim. The team has to have the cap space to accept his entire 15.3M salary this year, and is on the hook for the 16.8M next year. No one has enough cap space to do this (PHI has the most, with about 10M)
2) Partial claim. A team cap use whatever cap space they have between a "minimum partial bid" (in Boozer's case, 2 years of the vet minimum or 2.8M, of which 1.4M in cap room has to be available toward this year's cap) and their max cap space. Highest dollar amount wins.
3) No bid. In this case, once the player clears waivers he is a UFA just like regular waivers.
Coon CBA #67 talks more about amnesty