DISTRACTED BY A FUEL IMBALANCE; FA10 FLT CREW LANDS ON WRONG RWY AT MDW. COMPOUND ERROR BY TURNING ONTO AN INACTIVE RWY VICE CLEARED TAXIWAY.

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SIC WAS FLYING ACFT. WHILE VECTORED FOR THE APCH WE WERE CLRED TO FOLLOW A B737 FOR A VISUAL TO RWY 31C AT MDW AND TO SWITCH TO TOWER. IT WAS NOT A BUSY TIME. WHILE ALIGNING OURSELVES FOR THE SPACING AND OUTSIDE THE MARKER; WE SWITCHED TO TOWER AND THE CTLR ADVISED US THAT THERE WOULD BE AN ACFT DEPARTING BEFORE OUR LNDG AND HE MADE ANOTHER TRANSMISSION THAT SOUNDED LIKE WE NEEDED TO WATCH OUR BASE LEG TURN. I ASKED FOR A REPEAT AND BOTH CREW STILL WERE NOT TOTALLY CLR ON WHAT WAS SAID. WE SHOULD HAVE CLARIFIED. WE ASSUMED IT WAS REGARDING OUR SPACING BEHIND THE B737 IN ORDER TO FACILITATE DEP. AT THAT TIME WE WERE BUSY TRYING TO SLOW; CONFIGURE AND SPACE OURSELVES PROPERLY. AS WE CROSSED THE MARKER THE SIC STATED THAT SOMETHING DID NOT FEEL RIGHT AS EXCESSIVE RIGHT AILERON WAS NEEDED TO KEEP THE WINGS LEVEL AND WING UP TRIM WAS ADDED. THE PIC ASKED FOR A BRIEF TAKEOVER OF THE CONTROLS TO GET A FEEL FOR WHAT THE AIRPLANE WAS DOING AND AT THAT MOMENT WE RECEIVED A CLRNC TO LAND ON WHAT WE THOUGHT WAS RWY 31C. I REPEATED WHAT I BELIEVED WAS RWY 31C TO THE CTLR. AFTER A BRIEF TAKEOVER OF THE CONTROLS AND CONFIRMING THAT WE HAD A RIGHT WING HEAVY FUEL IMBALANCE CAUSING THE ROLL TENDENCY; THE PIC RETURNED CONTROL OF THE ACFT TO THE SIC FOR LNDG. I FELT THAT THIS WOULD BE GOOD EXPERIENCE FOR HIM. BY THIS TIME WE SAW THE DEPARTING ACFT TAXI ONTO THE RWY. WE WERE TIGHT ON SPACING AND BUSY SLOWING IN ORDER TO GIVE THAT ACFT TIME TO DEPART. I SHOULD HAVE CONFIRMED OUR RWY LNDG CLRNC. AFTER LNDG AND ROLL OUT; THE CTLR STATED THAT WE WERE CLRED TO LAND ON RWY 31R NOT RWY 31C. WE WERE TOLD TO TURN OFF AT TXWY A AND TO CONTACT GROUND. WHILE I WAS CONFUSED ON WHAT CAUSED THE ERROR; THE GROUND CTLR GAVE INSTRUCTIONS TO TAXI TO THE FBO. BECAUSE OF THE LACK OF FOCUS DUE TO THE RWY ERROR; A TURN WAS MADE ONTO A RWY 31L INSTEAD OF THE TXWY. THIS WAS AN INACTIVE RWY. WE WERE GIVEN INSTRUCTIONS TO GET ON THE PROPER TXWY AND RETURNED TO THE FBO. LESSONS LEARNED: CLARIFY WHAT THE CTLR SAYS EVEN IF IT MEANS 3-4 REPEATS. WHEN DISTRACTED ON APCH; RECONFIRM A LNDG CLRNC. IF AN INCIDENT OCCURS; DO NOT ALLOW IT TO TAKE YOUR FOCUS OFF COMPLETING THE TASK AT HAND.