LR55 CROSSED RWY AT TEB WITHOUT ATC CLRNC.

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AT APPROX XA10 WE WERE HOLDING SHORT OF RWY 24 AT TXWY G AS PER INSTRUCTIONS. AFTER HOLDING FOR SEVERAL MINS; WE RECEIVED A CALL OVER THE RADIO THAT SAID 'ACFT X; GO AHEAD AND GO' THIS SEEMED LIKE AN ODD XING CLRNC BUT AFTER OBSERVING AN AIRPLANE TURNING FROM RIGHT IN FRONT OF US ON THE RWY OFF ONTO THE TXWY ACROSS FROM US; AND NO AIRPLANES ON FINAL; IT SEEMED LOGICAL THAT THE CTLR WOULD WANT US TO FOLLOW THE OTHER AIRPLANE ACROSS. THERE WAS AN AIRPLANE AT THE END OF THE RWY APPROX 5000 FT AWAY THAT WAS PULLING ONTO THE RWY FOR TKOF. BECAUSE THE XING CLRNC SEEMED ODD; I READ BACK 'ACFT X XING RWY 24' AND LISTENED FOR THE CTLR TO SAY ANYTHING. THERE WAS NOTHING SAID SO I WRONGLY ASSUMED THAT I HAD RECEIVED A XING CLRNC. AFTER XING THE RWY; THE GND CTLR BEGAN YELLING AT US THAT WE CROSSED WITHOUT CLRNC. THE CTLR SAID THAT HE TOLD US TO 'DISREGARD' WHAT HE HAD SAID CONCERNING 'GO AHEAD AND GO.' THAT NEVER CAME OVER THE RADIO AND I ASSUME THAT IT WAS SAID WHILE I WAS READING BACK THE CLRNC. THE PROBS WITH THIS EVENT ARE THAT IT WAS A SUNDAY AND THERE WAS A PERCEPTION OF EVERYONE TAKING IT A LITTLE EASY; WHICH IS A REASON I THOUGHT THAT THE CTLR HAD WANTED ME TO CROSS WITH SUCH A WEAK SOUNDING CLRNC. ALSO; THE OTHER PLT ON BOARD WAS BUSY WITH OTHER THINGS SO DID NOT MONITOR THE FREQ TO XCHK WHAT WAS OCCURRING; BUT WAS OPERATING THE FLT CTLS AT THE TIME. IN ADDITION; THERE WAS ANOTHER FREQ BLEEDING OVER ONTO THE GND FREQ THAT WAS LATER IDENTED AS NEWARK GND CTL; WHICH WAS CAUSING BLOCKING OF XMISSIONS. IN THE END IT COMES DOWN TO NEVER ASSUME ANYTHING AND VERIFY EVERYTHING WITH PROPER PHRASEOLOGY. SUPPLEMENTAL INFO FROM ACN 612418: WE WERE HOLDING SHORT OF THE RWY AND THE GND CTLR DISTINCTLY SAID OVER THE RADIO; 'LEAR XXX; GO AHEAD AND GO.' WE CLRED L AND R; AND WERE FOLLOWING AN ACFT THAT HAD LANDED AND WAS TURNING OFF THE RWY THE OTHER DIRECTION. THERE WAS ANOTHER ACFT PULLING INTO POS 5000 FT DOWN THE RWY. WE READ BACK; 'LEAR XXXX; XING RWY 24.' THIS WAS APPARENT ON THE GND FREQ TAPE. BUT; DURING THE READBACK; THERE WAS A XMISSION ON THE FREQ THAT WAS UNINTELLIGIBLE. APPARENTLY; IT WAS THE CTLR SAYING 'DISREGARD;' WHICH NEVER CAME OVER THE RADIO. THE PHRASEOLOGY THAT THE CTLR USED WAS NOT CORRECT; AND WE SHOULD HAVE VERIFIED BEFORE XING.