In order to study the definition of Sin, here is a list of Greek words translated as sin:

1. ¢amartia - to miss the Mark
2. agnohma - an act done in ignorance of God's will
   1. Hebrews 9:7 (Sin committed in ignorance)
   2. 1 Timothy 1:13 (Sin committed in ignorance)
3. ¢uperbainw - going beyond the will of God
   1. 1 Thessalonians 4:6 (overstepping or trespass) in Josephus and Philo lit. "going beyond the head of the risen Lord."
4. skandalon - a cause of sinning or causing someone else to fail
5. enoicoV - guilty or liable
6. ponhroV - guilty or evil, as a noun one who has done an evil deed.
7. ptaiw - stumbling or failing to live up to God's will
8. proskomma - taking the opportunity to sin or cause someone to sin
9. paratoma - a transgression of the will of God

More information forthcoming.

Many of these words are only used once in the whole bible, so for a complete listing of how words were used by early Christians see:
A Greek-English lexicon of the New Testament and Other Early Christian Literature by Walter Bauer