FLC OF AN LGT ACR ACFT OVERSHOT DSCNT ALT RESULTING IN CAUSING EVASIVE ACTION IN RESPONSE TO TCASII RA'S.

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ENRTE FROM OMA TO DEN DURING A LARGE INBOUND BANK; WE RECEIVED VARIOUS ALT AND SPD CHANGES FROM ZDV. THEY CLRED US TO CROSS SMITY AT FL190 AT 250 KTS. DURING THE DSCNT WE ACKNOWLEDGED A CLRNC TO 15000 FT. APCHING SMITY AND FL190 WE SAW ON TCASII AND VISUALLY ANOTHER ACFT CONVERGING AT SMITY. RADIO CONGESTION WAS HVY AND WE COULD NOT GET VERIFICATION OF OUR CLRED ALT. TCASII WENT OFF AS WE LEVELED OUT AT ABOUT 18800 FT AND STARTED TO CLB BACK TO FL190. ANOTHER CTLR CUT IN AND ASKED OUR ALT AND SAID THAT WE WERE CLRED TO FL190. WHILE TRYING TO GET OUR PROPER ALT VERIFIED; WE RECEIVED A TCASII RA TO CLB; FOLLOWED IMMEDIATELY BY ONE TO DSND. WE WERE SANDWICHED BTWN AN ACFT AT FL180 AND FL200. THIS CONTINUED FOR 2-3 MINS; MAYBE; WHILE WE COMPLAINED ABOUT THE CONTINUOUS RA'S; WHAT OUR ORIGINAL CLRED ALT WAS AND WHAT CTR'S PHONE NUMBER WAS. THE ACFT ABOVE US WAS ALSO COMPLAINING ABOUT CONTINUOUS RA'S. CTR FINALLY GAVE US A VECTOR OUT OF THE STACK AND PUT US BACK IN LINE. IT APPEARED THAT THE CTLR WAS VERY NEAR TO BEING OVERLOADED WITH THE HVY INBOUND TFC. I THINK THE TCASII NEEDS TO BE MODIFIED SO YOU DON'T GET CONTINUOUS RA'S WITH NO CLB OR DSCNT INDICATED. ZDV HAS SINCE PULLED THE TAPES WHICH SHOW WE WERE CLRED TO FL250 INSTEAD OF 15000 FT. I MISUNDERSTOOD THE CLRNC AND READ BACK THE WRONG FLT LEVEL AND THE CTLR DID NOT CORRECT IT.