I will give you a quick answer for this, because I feel for you in your state of confusion! this can be a tough predicament, but this is really no predicament at all, like most seeming "contradictions" in the Bible, the problem is with our understanding, and not with the Bible itself.
A classic approach to attacking the Christian faith / Bible is to cherry pick verses out of the Mosaic Law that are particular out of place in our modern culture.
The idea is this, if the Christian agrees with the Scripture, then they are a labeled as hateful, bigotted, or possibly even criminal (which is what stoning a homosexual in the USA is, it is called murder.) So the Christian is put in a seeming dilemma, Either admit you are a murderous hateful biggot, OR admit that the Bible is wrong, and you are just a hypocrite. Either of these choices are ideal for the person who is attacking the faith/Bible.
But really we just need a better understanding of God's word to clear this all up.
Traditionally the Law of Moses is divided into 3 sections. The Ceremonial, Civil and Moral.
Basic over-view of each:
The Civil Law: Israel was LITERALLY a brand new nation. They needed laws, judges, and regulations of every kind. God gave this to them in a set of Civil laws, for the Jews, in the nation of Israel.
I am not a jew, but a Gentile, and I live not in Israel, but under another nation altogether, The United States. It is commanded clearly in the new testament that believers should behave orderly and not break the laws of the nation whenever possible. Think of Jesus statement about paying taxes, in
And He said to them, “Whose image and inscription is this?"
21 They said to Him, “Caesar’s.”
And He said to them, “Render therefore to Caesar the things that are Caesar’s, and to God the things that are God’s.” NKJV
Also see Paul in
Romans 13 :1-7 13 Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. 2 Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves. 3 For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same. 4 For he is God’s minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God’s minister, an avenger to execute wrath on him who practices evil. 5 Therefore you must be subject, not only because of wrath but also for conscience’ sake. 6 For because of this you also pay taxes, for they are God’s ministers attending continually to this very thing. 7 Render therefore to all their due: taxes to whom taxes are due, customs to whom customs, fear to whom fear, honor to whom honor.
So as long as we are not ordered by the goverment to do anything immoral, and are not ordered against worshipping God (This is another question in itself) We are to honor the Government's laws as good citizens. Note that he also says "He does not bear the sword in vain" The "power of the sword" AKA the ability to take life in punishment of crime is reserved to the governing authorities. And not for us as individuals, or even as a church whole.
OK so that basically answers your question. The Bible, when taken as a whole, does NOT order Christians to kill homo-sexuals. Quite the opposite, we should count homo-sexuals as people who need god's grace and the forgiveness freely offered to men because of the death of the God Man, Jesus the Christ on the cross for the salvation of sinners of all stripes, Of whom i am the chief! Praise God!
Just for completeness we will touch on the other two aspects of the law.
We no longer sacrifice sheep and goats have you ever noticed that? (would make for an interesting church service) This is because Jesus has FULFILLED the ceremonial portion of the law.
Hebrews 10:12-14 12 But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God, 13 from that time waiting till His enemies are made His footstool. 14 For by one offering He has perfected forever those who are being sanctified.
Colossians 2:16-17 So let no one judge you in food or in drink, or regarding a festival or a new moon or sabbaths, 17 which are a shadow of things to come, but the substance is of Christ.
Finally, the Moral Law.
Best shown in the 10 commandments. This aspect of the law stands for all time, Thats because it shows what God thinks is Good, and What is Bad. It is consistent with his Character, which never changes.
The Commandment says "You shall not bear false witness" Lying is wrong, because God is True.
The Commandment says "You shall not commit Adultery" Adultery is wrong, because God is Faithful. (adultery being unfaithful).
(You can find the 10 commandments in Exodus 20 if you are interested)
These things stand for all time!
Hope this helps you, and answers your question. Be encouraged, and continue to "Study to Show yourself approved"!