In 2003, we were launching our F-14D's out with mixed loadouts that included AIM-54C's on the port shoulder pylon. Stbd side was loaded with the LANTIRN Pod. I did not see any F-14's (or Hornets for that matter) leave the deck with a dedicated air to air loadout. The LANTIRN was always carried and was usually counterbalanced by an AIM-7 or AIM-54. I have never seen the 4 Sparrow 4 Winder loadout actually used but I know they can be loaded that way. If I were to take the Tomcat against other fighters a combination of AIM-7's and AIM-9's is the best bet (that is, in fact, what I take in WOX to perform fighter sweeps with the F-14).
The AIM-54 had some success in the Iran-Iraq war in the 80's but that was mainly due to the primitive ESM/ECM, generally poor command, communications, control and pilot training of the Iraqi Air Force. Iranian claims are many with at least two kills being acknowledged by the US. The truth is probably somewhere in the middle.
Here's a photo I took of one of our Tomcats returning from a patrol in 2005-6. Notice that it is only carrying two Sidewinders but is ready to have an AIM-7 loaded on the port shoulder pylon if needed. There was not much call for air to air weapons in Iraq at that time so they were left off to save their airframe hours. (yes missiles have airframe hours too)
This pic (not taken by me) shows the typical loadout for F-14 during the 2003 war. Sometimes it was an AIM-54 and sometimes it was an AIM-7 on this station.
Oh, and the AIM-54 was out of service in 2005.