ATX LTT DEVIATION FROM CLRNC ROUTE AFTER ENCOUNTER WITH ENROUTE WX TSTM ACTIVITY.

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I DEPARTED HNL IN AN LTT EBND FOR OAK ON R465 (CHARLIE TRACK). AFTER TKOF WE PROCEEDED NORMALLY. MY GNS CONCURRED WITH ATC'S GNDSPD READOUT; AS WELL AS MY POS OVER CLUTS; MY FIRST CHKPOINT. AT APPROX 130 DEGS W 2 DEGS BEFORE COSTS; I WAS IN CLOUDS SKIMMING THE TOP OF A CLOUD LAYER; IFR. MY RADAR HAD BEEN PICKING UP A RAINSHOWER 12 O'CLOCK AND CLOSING (50 MI INITIALLY). I RADIOED SFO THAT I WOULD LIKE TO DEVIATE N OF COURSE BUT COYLE NOT GET A RESPONSE FROM OCEANIC; I TRIED TWICE THE WX NOW SHOWED 15 MI AHEAD. I DECIDED TO TURN N TO AVOID THIS WX. THERE WAS A SIGMET OUT IN MY AREA FOR ISOLATED TSTMS AND SEVERE TURB. AS I INITIATED MY TURN MY GND 'D-R' WHICH MEANS BAD OR INAPPROPRIATE SIGNAL RECEPTION IT REMAINED IN 'D-R' FOR APPROX 14-16 MINS. AFTER CLRING I RESUMED NAV ACCORDING TO MY COMPUTER FLT PLAN AS WELL AS MY GNS WHICH NOW RETURNED TO VLF ON GOOD SIGNAL. HOWEVER; UPON REACHING CLUKK AND N360500 W 1245000 AN OAK CTLR RADAR IDENTED ME 23 MI OFF COURSE NW OF CLUKK. I TOLD HIM I WAS UNAWARE I WAS THAT FAR OFF COURSE; BUT TOLD HIM HOW I BELIEVED IT HAPPENED AND WHERE. I BELIEVE IF I COULD HAVE REACHED OCEANIC CTL EARLIER AND HAD STAYED FARTHER AWAY FROM THE WX MY GND WOULD NOT HAVE 'D-R' AND WOULD HAVE BEEN MORE ACCURATE. TSTMS CAN CAUSE FAULTY GNS READOUTS. SO; I BELIEVE TURNING SOONER WOULD HAVE KEPT MY GNS IN A GOOD NAV SIGNAL LOCK. I CHANGED MY DEST TO SJC AND LANDED THERE INSTEAD OF OAK. AS FAR AS I WAS INFORMED; THERE WERE NO OTHER ACFT IN MY AREA AT THE TIME. WE ARE AN AIR TAXI OPERATOR BUT WERE OPERATING PART 91 AT THE TIME.