AN UNSTABILIZED APCH IN GUSTY CROSSWINDS TO A SHORT RWY CONTRIBUTE TO C172 PLT'S INABILITY TO STOP ON THE REMAINING RWY. STRIKES REIL LIGHT WITH PROP DURING THE EXCURSION.

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I TOOK OFF FROM MY HOME BASE ON A LCL FLT TO ZZZ. WINDS AT A NEARBY FIELD WERE 260 DEGS AT 19 KTS GUSTING TO 24 KTS -- THERE IS NO AWOS/ASOS AT ZZZ. WHEN 4 NM OUT FROM ZZZ; I CALLED UNICOM FOR A LNDG ADVISORY. RWY 18 WAS RPTED AS THE ACTIVE WITH WINDS 270 DEGS AT 20 KTS. MY INITIAL APCH WAS HIGH; SO I WENT AROUND. ON THE SECOND APCH; I APPLIED 10 DEGS OF FLAP ON BASE; AND BEING SLIGHTLY HIGH ON FINAL APPLIED ADDITIONAL FLAPS UNTIL WAS DSNDING TOWARD THE NUMBERS; CRABBING INTO THE WIND. AT ABOUT 20 FT ABOVE THE RWY; I TRANSITIONED TO A SLIP AND WAS ALIGNED WITH THE RWY CTRLINE. UPON INITIATING THE FLARE; A STRONG WIND GUST CAUSED SIGNIFICANT PITCHING AND ROLLING MOVEMENTS OF THE ACFT; REQUIRING LARGE CTL INPUTS TO SETTLE THE PLANE ONTO THE RWY; ABOUT 1/2 WAY DOWN ITS 2300 FT LENGTH. BRAKES WERE APPLIED; BUT THE ACFT'S DECELERATION SEEMED TO TAKE MUCH LONGER THAN USUAL. I APPLIED THE BRAKES MORE AGGRESSIVELY; INTERMITTENTLY EXPERIENCING BRAKE LOCKUP. AS THE ACFT SLOWED TOWARD THE END OF THE RWY; THE RUDDER LOST EFFECTIVENESS AND THE STRONG XWIND CAUSED THE PLANE TO WEATHERVANE TO THE R OF RWY CTRLINE. THE PLANE; VEERING TO THE R OFF THE RWY END; THEN STRUCK A REIL. THERE WAS NO IMMEDIATE INDICATION THAT THE PROP HAD STRUCK ANYTHING -- THERE WAS NO ABNORMAL VIBRATION OR UNUSUAL NOISES. AFTER TAXIING BACK TO PARKING AND SHUTTING DOWN; INSPECTION REVEALED A DENT ON THE R GEAR LEG FAIRING; AND A DEEP NICK ON THE PROP; WHICH WE LATER LEARNED SLICED OFF A PIECE OF THE REIL'S LENS FLANGE. 1 FACTOR IN THE OVERRUN WAS THE INCREASED GND ROLL LIKELY DUE TO AN UNEXPECTED QUARTERING TAILWIND. AFTER PARKING; IT WAS NOTED BY SEVERAL PLTS PRESENT THAT OVER A 5 MIN PERIOD; THE WINDSOCK WOULD SHOW THE WIND VARYING FROM A WESTERLY DIRECTION TO A NW DIRECTION; BACK TO A WESTERLY DIRECTION; THEN TO A SOUTHWESTERLY DIRECTION; AND SO ON. THIS WOULD INDICATE THAT UPON MY FLARE; THE WIND PROBABLY SHIFTED SO I HAD A QUARTERING TAILWIND FROM THE NW. THIS INDICATION IS STRENGTHENED BY THE FACT THAT THE BRAKING DISTANCE WAS MUCH LONGER THAN EXPECTED. BASED ON MY CALCULATIONS; LNDG ON A HDG OF 180 DEGS WITH A 20 KT WIND AT 290 DEGS WOULD HAVE GIVEN ME A TAILWIND COMPONENT OF ABOUT 5 KTS (8 MPH) WHICH; BY MY ESTIMATE FROM THE POH DATA; WOULD HAVE INCREASED THE GND ROLL BY ABOUT 15%. AS IT HAPPENED; THE PLANE CAME TO A STOP WITH THE NOSE 50 FT FROM THE END OF THE RWY. THE SECOND FACTOR WAS THAT I DIDN'T FULLY APPRECIATE THE COMBINATION OF FACTORS THAT; TAKEN TOGETHER; MADE FOR A VERY DIFFICULT LNDG: 1) SHORT RWY. 2) STRONG 90 DEG XWIND WITH NO STABLE HEADWIND COMPONENT. 3) POTENTIAL FOR A WIND SHIFT TO A QUARTERING TAILWIND. 4) LACK OF RECENT EXPERIENCE LNDG AT ZZZ. 5) CARRYING TOO MUCH FLAP FOR THE STRENGTH OF THE XWIND. A THIRD FACTOR WAS MY CONTINUING THE LNDG AFTER THE FLARE ON A SHORT RWY WHEN THE PLANE DID NOT BEHAVE AS EXPECTED. PREVENTION: INCREASE AWARENESS BY USING A FORMAL CHKLIST FOR EACH FLT THAT REQUIRES WRITING DOWN ALL THE FACTORS THAT AFFECT THE LNDG AT ANY DEST ARPT: 1) RWY LENGTH. 2) XWIND DIRECTION/STRENGTH; AND ASSESSMENT FOR A POTENTIAL TAILWIND COMPONENT. 3) HEADWIND COMPONENT FOR EXPECTED CONDITIONS. 4) GND ROLL FOR EXPECTED CONDITIONS. 5) IDENT OF TOUCHDOWN POINT FOR A GAR DECISION. 6) MAX FLAP SETTING FOR GIVEN XWIND. 7) PERSONAL LIMITS FOR XWIND LNDGS BASED ON ABOVE FACTORS.