The USAF website, http://www.af.mil
, has a lot of answers to your question, but briefly--SAC hasn't existed since the mid-1990s. The aircraft and flying units that used to belong to SAC now are a part of Air Combat Command (ACC). In the event they have to perform a strategic nuclear mission they would come under the operation control of U.S. Strategic Command, the warfighting command made up of the three parts of the nuclear "triad"--land-based ICBMs, manned bombers, and Sea-launched ballistic missile (SLBMs). It is a joint command made up of Air Force and Navy personnel. Day-to-day operational control of ICBMs is handled by USAF Space Command.
Curently in the inventory there are: