Oldham rhymes with:
earldom, hildum, officialdom, seldom, adam, addendum, afrikanerdom, boredom, cadam, carborundum, chiefdom, christendom, condom, corundum, dedham, dukedom, earldom, edam, fiefdom, fordham, freedom, gaddum, hildum, kingdom, leedom, macadam, madam, madame, martyrdom, mcadam, memorandum, modem, needham, nydam, odom, odum, officialdom, purdham, purdom, purdum, random, referendum, rodham, saddam, sandom, sedam, sedum, seldom, sheikdom, sodom, stardom, subkingdom, suydam, tandem, windham, windom, wisdom, wyndham
Oldham sounds like:
oldani, olden, oldman, oltman, oltmann