GEAR WOULD NOT RETRACT AFTER TKOF; WOULD NOT EXTEND BY NORMAL OR ABNORMAL PROCS; AND THE ENG QUIT PRIOR TO LNDG. AN ENG OUT PARTIALLY EXTENDED GEAR EMER LNDG WAS MADE FOLLOWED BY THE RPTR BEING INJURED IN THE EMER EVAC.

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I ACCOMPANIED MY MULTI-ENG INSTRUCTOR WHO WAS MOVING A C310 FROM FLORIDA TO WISCONSIN. A THOROUGH MAINT LOG ASSESSMENT AND VISUAL INSPECTION WERE MADE OF THE ACFT PRIOR TO DEP. AFTER A POSITIVE CLB RATE WAS ESTABLISHED; THE PIC BROUGHT THE GEAR UP. GREEN LIGHTS AND IN-TRANSIT LIGHTS APPEARED TO BE OPERATING NORMALLY. A FEW SECONDS LATER; TWR INFORMED US THAT THE NOSE AND R MAIN GEAR APPEARED TO BE ONLY HALF-WAY RETRACTED. TWR REQUESTED WE MAKE R TFC AND FLY BY SO THEY COULD GET A BETTER LOOK AT THE GEAR. AT THAT TIME; WE SMELLED THE ODOR OF BURNING ELECTRICAL WIRE. THE PIC RECYCLED THE GEAR. IT DID NOT COME DOWN. PLTS OPERATING HANDBOOK PROCS FOR EMER GEAR EXTENSION WERE FOLLOWED; HOWEVER; UNSUCCESSFUL. THE PIC DECIDED TO CONTINUE THE FLT TO BURN OFF FUEL BEFORE MAKING THE GEAR-UP LNDG. THE CTLR CLRED US TO FLY AT 1500 FT. THE PIC DECLARED AN EMER. GEAR FAILURE EMER CHKLISTS WERE REVIEWED. AFTER APPROX 3 HRS OF CIRCLING THE ARPT; THE L ENG FAILED. ENG OUT EMER CHKLIST WAS FOLLOWED. THE PIC LANDED THE ACFT SINGLE ENG; NO GEAR. SOUNDS OF METAL WERE HEARD SCRAPING ACROSS THE RWY AND WE FEARED FIRE AS THERE WAS APPROX 3 HRS FUEL REMAINING ONBOARD. THE ACFT VEERED TO THE R OFF THE RWY COMING TO A STOP HALFWAY IN THE GRASS. IN EVACUATING THE ACFT I FELL FRACTURING MY R FOOT AND INJURING MY R ROTATOR CUFF. IN TERMS OF HUMAN PERFORMANCE; REMAINING CALM; FOLLOWING CHKLISTS AND THE PLTS OPERATING HANDBOOK; TRAINING AND EXPERIENCE WERE THE KEYS. FRUSTRATION WAS ADDED; HOWEVER; BY TRYING TO LISTEN TO A CUBAN MECH WHO DID NOT SPEAK CLR ENGLISH AND WHOM COULD NOT BE UNDERSTOOD OVER THE RADIO; AND USING AN EMER GEAR EXTENSION SYS THAT DID NOT WORK.