WRONG RWY APCH BY SMT PLT.

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DEPARTED LAS VEGAS (L15) ON IFR FLT PLAN TO LONG BEACH; CA. FLT WAS ROUTINE EXCEPT FOR SANTA ANA WINDS AND TURB OVER THE MOUNTAINS. LONG BEACH WAS USING THE NDB RWY 30. I WAS HAVING PROBS WITH THE NEEDLE; AS IT WOULD STICK. HOWEVER; IT WAS CLR AND WE HAD RADAR VECTORS TO FINAL. APCH TOLD US TO EXPECT RWY 25. WHEN TURNED OVER TO TWR; THEY GAVE US SEVERAL CLOSE TARGETS TO LOOK FOR; ASSIGNED US RWY 7R. WHILE STILL DISTRACTED BY THE ADF NEEDLE; LOOKING FOR THE SLOWER TFC; I INADVERTENTLY LINED UP WITH RWY 34R. ON FINAL; TWR ASKED US OUR INTENTIONS (A CLUE); I SAID TURNING FINAL FOR RWY 7R. AFTER A SHORT TIME; TWR INFORMED ME I WAS ALIGNED WITH RWY 34R; CALLED SOME HELI TFC AT 12 O'CLOCK; WHICH I SAW AND THEN REALIZED MY ERROR. AFTER CALLING ANOTHER ACFT TO MY ATTN (NO FACTOR) CLRED ME FOR A L DOWNWIND TO RWY 7R. NO FURTHER MENTION WAS MADE OF MY ERROR. CORRECTIVE ACTION WAS TO PUT FULL ATTN TO THE LNDG PHASE. A SIMPLE XCHK OF THE HDG INDICATOR WOULD HAVE AVOIDED THIS. I SIMPLY VISUALLY SAW A RWY AND ASSUMED IT WAS THE CORRECT ONE.