WITH MULTIPLE COM PROBS A B727 CREW COORDS WITH THEIR DISPATCHER AND PROCEEDS TO A DIVERSION STATION.

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CRUISING AT FL350 NEAR IIU; ATC NOTIFIED US THAT OUR RADIOS WERE FULL OF STATIC AND ALMOST UNREADABLE. SUSPECTING A BAD MIKE; THE CAPT SUBSTITUTED ANOTHER MIKE FOR HIS AND REATTEMPTED TO CONTACT ATC STILL USING THE #1 RADIO. XMISSION WAS STILL UNREADABLE AND THE #2 RADIO WAS TRIED. IT; TOO; WAS UNREADABLE. THE FO ATTEMPTED CONTACT WITH HIS MIKE AND THAT; TOO; WAS UNSUCCESSFUL. THE SO ALSO TRIED TO CONTACT ATC ON RADIOS #1 AND #2 AND WAS ALSO UNSUCCESSFUL. WE COULD HEAR ATC ON BOTH RADIOS; BUT THEY COULD NOT HEAR OUR RESPONSE. WE SENT AN ACARS MESSAGE TO MSP DISPATCH INFORMING THEM OF OUR PROB AND ASKING THEM TO CONTACT ATC AND INFORM THEM OF OUR PROB. WE PROCEEDED ON OUR FLT PLAN AS FILED ACKNOWLEDGING FURTHER ATC INSTRUCTIONS WITH AN IDENT. WE THEN TESTED THE #3 RADIO AND FOUND THAT IT; TOO; WAS INOP WITH OUR HANDHELD MIKES. FINALLY; WE ATTEMPTED TO COMMUNICATE WITH CTR USING THE MIKES IN OUR OXYGEN MASKS AND DISCOVERED THAT THE CAPT'S MIKE WORKED ON BOTH RADIOS #1 AND #2. CONSEQUENTLY; VERBAL COM WAS RE-ESTABLISHED WITH ATC. WITH THE CONCURRENCE OF MSP DISPATCH; WE DECIDED TO LAND AT MSP. FURTHER RADIO COM WITH ATC USING THE CAPT'S OXYGEN MASK MIKE WAS SUCCESSFUL; AND THE LNDG WAS UNEVENTFUL.