CAPT OF AN MDT INADVERTENTLY TAXIED ACROSS RWY WITHOUT CLRNC DURING TAXI FOR TKOF.

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LEAVING THE GATE AT TULSA; OK; ARPT: CALL TWR FOR TAXI CLRNC. CTL SAID TAXI 8 (RWYS 18L AND 36R WERE CLOSED ALONG WITH SOME TXWYS) BEGIN TO TAXI OUT TO RWY 8 MADE A L TURN STARTED DOWN TXWY; COULD SEE A STRAIGHT LINE OF BLUE LIGHTS ALL THE WAY TO THE END. CALL FOR THE F10 TO DO FIRST FLT OF THE DAY AS WE WERE TAXIING I WAS MONITORING THE CHK SOMEWHAT. I DIDN'T REALIZE WE WERE TAXIING ONTO RWY 8. (IT WAS STARTING TO GET DAYLIGHT; RWY LIGHT WERE NOT REAL BRIGHT.) I NOTICED WE WERE ON THE RWY. LOOK SEE; NO ACFT. CALL TWR SAID WE HAD CROSSED RWY 8 ASK FOR HELP FOR THE PROPER TXWY. HE SAID TO DO A 180 DEG ON THE TXWY AND CROSS RWY 8 MAKE A R TURN ON THE FIRST TXWY AND TAXI TO THE END FOR RWY 8. 1) THIS WAS THE 4TH NIGHT ON CONTINUOUS DUTY FLT; WE GOT DUTY IN AT XK10 WENT TO HOV FIRST. THEN TO TUL. TO TUL AT XA05. RPTED BACK TO THE ACFT AT XE50 FOR ME AND MY FO. WE HAD THE SAME TRIP ALL MONTH. 2) TIME OF MORNING DUE TO LIGHTING AT THE ARPT RWYS AND TAXI LIGHT WITH A STRAIGHT TXWY XING A RWY. THE SPACING IS JUST ABOUT R DISTANCE BTWN THE BLUE TAXI LIGHT AND DID NOT NOTICE WE WERE ENTERING THE RWY UNTIL WE HAD ALREADY DONE SO. 3) ONLY ONE CTLR MANNING TWR WORKING GND AND RWY SAME TIME GIVING DEP CLRNCS. UNABLE TO MONITOR ACTIVITIES ON THE ARPT AT ALL TIMES. 4) WITH THE RWYS BEING CLOSED ALONG WITH TXWYS SOME MISUNDERSTANDING AS TO JUST WHAT WAS TO BE USED. 5) ALSO BAD TIMING ON DOING AUTOFEATHER CHK. NO OTHER ACFT WERE INVOLVED IN THE OCCURRENCE.