PLT OF ATX CLRED FOR TKOF AT LAX RWY HDG. AFTER TKOF TWR CLRED L TURN TO 200 DEGS. PLT HELD PREVIOUS CLRNC RWY HDG. ADVISED CALL TWR SUPVR ON LNDG.

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FOR TKOF I REQUESTED AN 'IFR TO VFR' ON TOP CLRNC; SINCE HVY GND FOG WAS APCHING THE ARPT FROM THE W. I RECEIVED MY CLRNC; AND WAS TOLD BY LAX GND CTL TO TAXI TO 25L. UPON REACHING THE HOLD LINE AT 25L; THE TWR INFORMED ALL AIR AND GND TFC THAT THE LIGHTS FOR 25L WENT OUT. THIS SITUATION SEEMED TO CREATE A CHAOTIC SITUATION; SINCE THE WX WAS DETERIORATING BY THE MIN. WHILE I WAS WAITING FOR TKOF; I RECEIVED A SECOND 'IFR TO VFR' ON TOP CLRNC. THE CLRNC CALLED FOR MAINTAINING RWY HDG (250 DEGS) AFTER DEP. SHORTLY AFTER I WAS ISSUED A TKOF CLRNC FOR RWY 25R. AFTER I BECAME AIRBORNE; THE TWR TOLD ME TO TURN L TO A HDG OF 200 DEGS. THIS HDG CONFLICTED WITH THE INFO THAT I HAD RECEIVED ON MY SECOND 'IFR TO VFR' ON TOP CLRNC. I WANTED TO CALL THE TWR FOR CLARIFICATION BUT THE FREQ WAS TOO CONGESTED TO 'BREAK IN.' I CONTINUED TO FLY THE HDG THAT I WAS ASSIGNED. THE TWR CAME BACK AGAIN AND REQUESTED THAT I TURN L TO A HDG OF 200 DEGS IMMEDIATELY. I COMPLIED WITH THE TWR AND TURNED TOWARD THAT HDG. SHORTLY THEREAFTER; THE TWR INSTRUCTED ME TO TURN TO A HDG OF 180. I ENTERED A STEEP TURN TO THE L AND TURNED TO 180; COMPLYING WITH THE TWR'S INSTRUCTIONS. A SHORT TIME LATER; TWR ADVISED ME TO CONTACT LOS ANGELES DEP CTL. AFTER CONTACTING DEP CTL; I ELECTED TO CANCEL MY IFR CLRNC; SINCE I WAS IN VMC CONDITIONS. I RECEIVED VECTORS FROM DEP CTL AND WAS CLRED THROUGH THE TCA WITHOUT FURTHER INCIDENT. AS I WAS APCHING OXNARD; LOS ANGELES DEP ADVISED THAT I WAS EXITING THEIR AIRSPACE. DEP CTL TOLD ME TO CONTACT LAX TWR AFTER I LANDED AT SANTA MARIA. AS SOON AS I LANDED AT SANTA MARIA; I CONTACTED LAX TWR AND SPOKE WITH SUPVR WHO WAS RELUCTANT TO GIVE ME ANY INFO STATING 'THIS INCIDENT WILL BE INVESTIGATED BY THE LOS ANGELES FLT STANDARDS DISTRICT OFFICE.'