None of those words tossed about are linguistically rooted in the Holy Scriptures. Sodomy and sodomite were coined by the church in the 13th century and have had various meanings attached to them through the centuries. At one time sodomy was any sexual act that was not procreative, so sex for pleasure even between husband and wife was sodomy. The words homosexuality and homosexual were coined in the late 19th century and have no equivalent in the Holy Scriptures as well. To understand the meaning of "sodomite" as used in 1 Cor. 6:9 and 1 Tim. 1:10 in many more modern translations you must go with shades of meaning as seen in the Roget's Thesaurus.
"The terms 'homosexuality' and 'homosexual' are coinages of the 19th century C.E. and have no equivalent in ancient Hebrew or Greek. It is debatable whether the modern idea of homosexuality (an erotic attraction focused only or primarily on persons of the same gender) existed at all in antiquity. The Bible does not appear to say anything directly about homosexuality in this modern sense of the term, but a few passages do refer to same-gender genital acts." Eerdman's Bible Dictionary, 2000c
"The terms 'homosexuality' and 'homosexual' are coinages of the 19th century C.E. and have no equivalent in ancient Hebrew or Greek. It is debatable whether the modern idea of homosexuality (an erotic attraction focused only or primarily on persons of the same gender) existed at all in antiquity. The Bible does not appear to say anything directly about homosexuality in this modern sense of the term, but a few passages do refer to same-gender genital acts." Eerdman's Bible Dictionary, 2000c