C150 PLTS ON A VFR FLT ENCOUNTER SOLID UNDERCAST AND CONTINUE THE FLT INTO CLASS C AIRSPACE.

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I WAS THE PIC. THE ACFT OWNER; WHO IS A VERY EXPERIENCED PLT; WAS RIDING IN THE R SEAT. SINCE HE DOESN'T CURRENTLY HAVE A MEDICAL CERTIFICATE; HE LETS ME SIT IN THE L SEAT AND DO THE FLYING. THE PLAN WAS TO FLY FROM A PVT GRASS STRIP TO AN ARPT NEAR SYRACUSE; NY. THERE WAS A LOT OF FOG IN THE AREA THAT MORNING. BUT IT WAS CLR AT THE FIELD. MY COPLT FELT THAT WE COULD TAKE OFF; AND WE WOULD FIND THAT THE FOG WAS SCATTERED WITH LOTS OF OPEN BREAKS. I TENDED TO CONCUR WITH HIM. OUR EXPERIENCE THE PREVIOUS MORNING HAD BEEN LIKE THAT; AND BY THE TIME WE TOOK OFF THERE WAS VERY LITTLE FOG AND JUST A MODERATE AMOUNT OF HAZE. SOON AFTER TKOF WE FOUND THAT THERE WAS A LOT OF FOG. LARGE AREAS OF THE GND WERE COVERED. WE HAD TO STRUGGLE TO IDENT THE SMALL TOWN LOCATED 3 MI FROM THE DEP ARPT. BUT FOR VARIOUS REASONS WE DIDN'T TURN BACK. THE SKY ABOVE THE FOG WAS SMOOTH AND CLR; AND WE COULD SEE SOME BREAKS IN THE FOG IN THE DIRECTION WE INTENDED TO HEAD. SO I TOOK UP A HDG FOR OUR DEST; AND CONTINUED. USUALLY WE USE PILOTAGE TO NAV TO OUR DESTS. BUT WITH THE FOG LAYER I REALIZED THAT WE WERE GOING TO HAVE SIGNIFICANT TROUBLE KEEPING TRACK OF OUR LOCATION. MY COPLT STARTED TRACKING OUR PROGRESS BY TAKING XBEARINGS OFF OF THE ROCHESTER VOR. SINCE THIS WASN'T ENOUGH TO FULLY DETERMINE OUR LOCATION; I REALIZED THAT WE WERE AT RISK OF VIOLATING THE ROCHESTER CLASS C AIRSPACE. SO I CONTACTED ROCHESTER APCH. FOR A WHILE THERE WAS NO FOG BELOW US; AND WE COULD NAV EASILY. BUT FOR MOST OF THE LAST 30 MI OR SO; WE WERE FLYING OVER A SMOOTH; SOLID LAYER OF FOG THAT TOTALLY OBSCURED THE GND. I STARTED USING VOR XBEARINGS OFF OF BOTH THE SYRACUSE AND ITHACA VORS TO VERIFY OUR POS. ABOUT 10 MI SW OF OUR DEST; WE DID SEE 1 OPEN AREA; WHICH I IDENTED (RIGHT OR WRONG) AS THE CITY OF AUBURN. BUT THAT WAS OUR ONLY CONFIRMATION OF OUR POS. I CONTINUED TO USE THE VOR TO NAV; UNTIL WE HAD ARRIVED AT THE COORDINATES THAT SHOULD HAVE PUT US OVER THE DEST. THERE WAS SOLID FOG; SO WE DIDN'T DSND. WE THEN TURNED AND HEADED BACK TOWARD THE AREA WHERE WE HAD LAST HAD GND CONTACT. AFTER THE FLT; IT OCCURRED TO ME THAT I HAVE NEVER CONFIRMED THE ACCURACY OF THE VOR RECEIVER IN THIS AIRPLANE. ALSO; SINCE WE WERE FLYING RATHER LOW; IT IS REASONABLE TO QUESTION THE ACCURACY OF THE SIGNAL WE WERE RECEIVING FROM THE 2 VOR STATIONS I WAS USING. SO THE NET RESULT IS THAT I REALLY DIDN'T KNOW IF WE WERE OVER OUR DEST OR NOT. WE COULD HAVE EASILY BEEN SEVERAL MI TO THE E; IN WHICH CASE WE COULD HAVE VIOLATED THE SYRACUSE CLASS C AIRSPACE. THERE WERE MANY OPPORTUNITIES TO PREVENT THIS FROM HAPPENING. WE NEVER SHOULD HAVE TAKEN THIS FLT. WE COULD HAVE TURNED BACK AT ANY TIME. BUT ONCE WE TOOK OFF; I JUST KEPT GOING.