ERJ FLT CREW RWY EXCURSION ON WET RWY IN GUSTY WIND CONDITIONS. MINOR DAMAGE TO ACFT AND TXWY LIGHT.

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AS WE APCHED ZZZ; NORMAL CALLS WERE MADE TO COMPANY. OPS INDICATED LIGHT RAIN ON THE AIRFIELD WITH NO TFC IN THE AREA. DISPATCH ADVISED US VIA ACARS THAT TSTMS WERE 35 MI W; WHICH AGREED WITH OUR WX RADAR. RADAR INDICATED LEVEL 1 AND LEVEL 2 ECHOS IN THE VICINITY. THE LOC DME BACK COURSE RWY 13 APCH WAS REQUESTED AND VECTORING BROUGHT US INTO A NORMAL APCH. AT THE FINAL APCH FIX INBOUND RWY 13 WAS SIGHTED AND CALLED FOR VISUALLY. APCH AND RAIN WERE EXPERIENCED DURING FINAL. VISUAL CONTACT WAS MAINTAINED THROUGHOUT THE APCH FROM THE FAF TO LNDG. APCH WAS CONTINUED USING LOC AND VASI. LIGHT TURB WAS NORMAL WITH THE EXCEPTION OF A SINK RATE CALL AT APPROX 500 FT AFL. I IMMEDIATELY CHKED INSTS; FO RESPONDED; 'I AM CONFIDENT TO CONTINUE;' ALL INDICATIONS WERE NORMAL AND THE ACFT WAS IN A SAFE LNDG ATTITUDE; CONFIGN; AND POS TO LAND; SO THE APCH WAS CONTINUED. LNDG WAS ON THE TOUCHDOWN ZONE AND ON CTRLINE. NOSEWHEEL TOUCHED DOWN AND REVERSERS WERE DEPLOYED. AT APPROX 80-100 KIAS; SOME 1500-2000 FT AFTER TOUCHDOWN; THE ACFT STARTED MOVING L. I MADE 2 CALLS TO CORRECT TO THE R AND TOOK CTL OF THE ACFT; ENSURING R RUDDER WAS APPLIED; YOKE WAS FORWARD AND R AND THRUST REVERSERS WERE MAX REVERSE. ACFT CONTINUED MOVING L. WE DEPARTED THE RWY BTWN 40-60 KIAS AND THE ACFT STOPPED IN THE SOD ON THE N SIDE OF RWY 13. IMMEDIATELY ASSESSED THE SIT; NOTIFIED OPS; AND ADVISORY (CFR). FIRE TRUCKS CAME TO INSPECT THE ACFT. I THEN CALLED THE FLT ATTENDANT; AND ASKED IF SHE AND THE PAX WERE OK AND TOLD HER TO REMAIN ABOARD THAT WE WOULD NOT EVAC AT THIS TIME; BUT TO WAIT FOR DEPLANING BY STAIRS. OPS AGENTS CAME WITH STAIRS; PAX WERE DEPLANED WITH NO FURTHER INCIDENT AND NO INJURIES WERE RPTED. UNSOLICITED RPTS FROM A NUMBER OF PARTIES INDICATED A VERY STRONG GUST OCCURRED AT THE ARPT AT THE TIME OF OUR LNDG. SUPPLEMENTAL INFO FROM ACN 635804: POSTFLT INSPECTION REVEALED DAMAGE TO THE R NOSEWHEEL AND ONE TAXI LIGHT.