INSTRUCTOR WITH SPI HAS RWY EXCURSION AND POOR DEP DUE TO MALFUNCTIONING RADIO.

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CLASS B AND C TRAINING FLT WITH STUDENT PLT. LANDED OAK FOR CLASS C DEP COMS PROCS (ATIS; CLRNC DEL; GND; TWR; ETC). OFF 27R TAXIED BACK TO RUN-UP AREA RWY 27R TO USE RADIO IN 7ECA. RADIO WAS OLD. IT WORKED FINE IN FLT THROUGH LNDG AND TAXI. RECEIVED ATIS. SWITCHED TO CLRNC DEL AND COULD NOT COM WITH MANY TRIES FROM BOTH MIKE POS. SAME PROB USING GND FREQ. SWITCHED BACK TO TWR (LCL) FREQ; EXPLAINED PROB AND ASKED FOR CLRNC TO PAO. RECEPTION WAS FAIR AND CTLR GAVE CLASS C DEP CLRNC AND XPONDER CODE AND TAXI CLRNC TO RWY 27R. I READ BACK CLRNC WITH POS AND HDG RWY 27R (I THOUGHT I HAD HEARD 'ONTO RWY 27R.') THE CTLR HAD MADE SOME 'NONSTANDARD' ATC CLRNCS SINCE OUR ARR; SO WITH THE COMBINATION OF A BAD RADIO; NON-STANDARD ATC COMS; I HEARD 'TAXI ON TO RWY 27R.' SO WE (ME AND STUDENT) DID. THE CTLR TOLD US HE HAD NOT CLRED US ONTO THE RWY; BUT TO RWY 27R (NO 'HOLD SHORT OF'). HE THEN CLRED US FOR TKOF ON 27R AND; EVIDENTLY; TO MAKE A R 270 DEG OVERHEAD 'DEP' WHICH I NEVER HEARD. SO I CALLED HIM ON UPWIND AT APPROX 500 FT AGL ASKING FOR FURTHER CLRNC. HE TOLD ME HE HAD SAID TO MAKE A 270 DEG OVERHEAD DEP. NO CONFLICTS FROM ANY OF THIS AS WE CLRED THE APCH PATH VISUALLY BEFORE AND AS WE TAXIED INTO POS. WITH THE DISTR OF A BAD RADIO; A STUDENT; AND A NON- STANDARD CTLR; I COULD HAVE EASILY MISUNDERSTOOD THE CTLR'S COMS/INTENTIONS. AS SOON AS WE WERE AIRBORNE; THE RADIO WORKED FINE. IT IS SCHEDULED TO BE REPAIRED WITH A HIGHER PERFORMANCE MODE IN 7 DAYS.