Thank you for your question, and I rejoice at your desire to have a clear translation of God's Word.
Most modern translators are caught between giving a literal translation that might be misleading and using contemporary terminology. You are correct that the term homosexual was not in use at the time the NT was written. In fact, though the practice was known (and generally approved of in the Greek world), Paul is more graphic in his language than the general term homosexual indicates. You will note that the text you cited has both the fourth and fifth terms that refer to aspects of what we generally call homosexual. This is because the Greek, like many other languages, has different terms for the active and the passive roles in this sin. The first term is sometimes translated effeminate, and designates the passive/receptive partner in the relationship. The second term, translated as sodomites in the NKJV, specifies the active partner in the homosexual relationship.
Proper and polite English doesn't have the matching words for the two roles, so the English Standard Version (for example) gives only the word "homosexual" as the translation for both words. Paul's emphasis is that no one who is sexually immoral, whether as in the sexually immoral (pornea), adultery (married individual), or any homosexual role, can claim to be an inheritor of the Kingdom of God. This doesn't mean that a Christian never sins sexually, but that the work of the Spirit of God applying the salvation given us in Jesus Christ leads to repentance from all such sins to the extent that they do not mark the life of a believer.
I hope this is helpful. Thank you again for wanting to have a full understanding of God's Word; may he continue to bless you with that hunger!
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