ATX PLT OF A BEECH BARON; BE58; LOST CTL OF ACFT ON A WET TXWY RESULTING IN SKIDDING OFF THE RWY AND BECOMING STRANDED.

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LANDED AT MSY ON RWY 1 AND TURNED OFF AT RWY 24; WAS TAXIING TO HOLD SHORT OF RWY 10. GND CTLR SAID TO KEEP THE SPD UP; CROSS RWY 10; ACFT ON 2 MI FINAL. I INCREASED SPD TO CROSS THE RWY. I TRIED TO SLOW DOWN TO TURN ONTO TXWY E WHEN I BEGAN TO HYDROPLANE (AND OR SKID) AND COULDN'T STOP IN TIME. I WENT THROUGH THE TXWY ONTO THE OVERRUN AREA (FOR RWY 24) AND STOPPED WITH THE NOSEWHEEL IN THE GRASS. I TRIED TO TURN AROUND AND GET BACK ON THE TXWY BUT ENDED UP GETTING THE R MAIN TIRE STUCK IN THE MUD AS WELL. I HAD TO BE TOWED OUT. CONTRIBUTING FACTORS: TAXIING TOO FAST -- DUE IN PART TO THE WIDTH OF THE RWY - - LACKED THE SENSATION OF SPD; ESPECIALLY AT NIGHT. FIXATION ON THE LNDG ACFT INSTEAD OF MY POS ON THE RWY. NIGHT; RAINING -- REDUCED VISIBILITY. WET PAVEMENT. POSITION AWARENESS -- DIDN'T REALIZE THE TXWY WAS SO CLOSE TO THE RWY I WAS XING. KEPT THE SPD UP TOO LONG. LACK OF TAXI LIGHTS ON THE OVERRUN; THE OVERRUN PORTION OF RWY 24 EXTENDS SLIGHTLY PAST TXWY E. WHERE THE OVERRUN AND TXWY INTERSECT THERE ARE NO TAXI LIGHTS. INSTEAD THERE IS PVC PIPE ABOUT 8 INCHES HIGH PAINTED BLUE (POSSIBLY REFLECTIVE) WHERE THERE SHOULD BE TAXI LIGHTS. (THE TAXI LIGHTS EXTEND ON BOTH SIDES OF THE OVERRUN). THIS GIVES THE ILLUSION THAT THE PAVEMENT CONTINUES (UNTIL YOU ARE VERY CLOSE AND CAN SEE THE PVC). THIS ILLUSION IS FURTHER ENHANCED BY THE TAXI LIGHTS THAT BORDER THE RAMP; JUST BEYOND THE OVERRUN (THE OVERRUN AND THE RAMP ARE SEPARATED BY A GRASS AREA); BECAUSE IT LOOKS LIKE THAT (THE RAMP) IS THE END. IN FACT IT LOOKS LIKE YOU CAN TAXI RIGHT ONTO THE RAMP FROM RWY 24. I THINK THE PVC 'TAXI MARKERS' SHOULD BE REPLACED WITH RECESSED TAXI LIGHTS.