Sin is a 'transgression of a religious or moral law, especially when deliberate', often regarded as either 'deliberate disobedience to the known will of [the Abrahamic] God, or 'a condition of estrangement from [the Abrahamic] God resulting from such disobedience'. I am not a Christian, nor was I raised as one, but in my opinion, sinful acts are acts which turn the actor away from the goal of Heaven; food, for example, if not a part of heaven, so to gutonously eat while here on earth shows you don't really want to get into heaven after all.

Once sinned, a devotee is barred from Heaven--the supreme goal--until he or she repents. Repenting is 'to feel remorse, contrition, or self-reproach for what one has done or failed to do', and includes 'an admission of guilt for committing a wrong or for omission of doing the right thing; a promise or resolve not to repeat the offense; an attempt to make restitution for the wrong, or in some way to reverse the harmful effects of the wrong or the omission where possible'. As Frank Stagg says:

"It is a call to conversion from self-love, self-trust, and self-assertion to obedient trust and self-commitment to God. It is a change of mind that involves a conscious turning away from wrong actions, attitudes and thoughts that conflict with a Godly lifestyle and biblical commands, and an intentional turning toward doing that which the Bible says pleases God."

 Naturally, sin has no place in Hellenismos, as well as modern Pagan religions, and yet, the concept lives on in its practicioners. I happened across another example a little while ago where guilt and fear over wrongdoing (in this case concerning a lack of daily--or at least consistant--ritual). Sin was never brought up, and this is my interpretation, but I still see it a lot around the Pagan internet hangouts: a fear to 'do wrong' that is beyond the scope of Hellenismos.

There are things you can 'do wrong' in Hellenism, but because of the way the concept of sin works, it can never be applied to the Hellenic religion: we are not working towards the goal of an afterlife. We know that we will inevertably end up in the realm of Hades, and it is nothing to look forward to. Only if you have done something incredibly inexcusable (kill, chop up and serve your son to the Theoi, for example, as Tantalos did), you might be punished in Tartaros. In general, we will walk the dreary Fields forever, while some of us--those who have done extraordinary deeds in life--will end up in Elysium, but that is a rare honor indeed.

Within Hellenismos, we try not to do wrong--or better, we always try to do right--by the Gods. They are the major influence over our lives, and we live largely by Their will. As such, fear of the Gods is a cornerstone of the faith, but it is not meant in the Christian sense where any sin committed is seen by God, and jeopardizes you place in heaven; here it is meant as a reminder of kharis: that the Gods look favorably upon those who honor Them properly. The implication here is, of course, that they do not look favorably upon those who do not honor Them properly, and this is correct, yet, committing hubris does not automatically mean that you will be punished by the Theoi; it simply means a drop in kharis.

Within Hellenic practice, miasma describes the lingering aura of uncleanliness in regards to a person or space through which contact is made with the Gods. Next to piety, being ritually clean is one of the most important things to adhere to within Hellenismos. We all incur miasma, every single day of our lives. It is a consequence of living. We breath, make decisions, come in contact with others, and along the way, we become too human--for lack of a better term--to petition the Gods. The divide between the purity and cleanliness of the Theoi and our human mortality and imperfection, keeps us away from Them.
There are striking similarities between the previous paragraph and the first I posted: a divide of 'human-ness' between humanity and divinity, a transgression against the Gods, a typically human act... but the differences that are telling: miasma and hubris do not require guilt to absolve. There is no need to repent and beg the Gods for forgiveness: Hellenismos blows by that part of repentance and goes straight to a change in behavior. Acknowledging your error is important, and sacrifices are often given, but miasma is 'absolved' often by washing and cleaning alone, and a drop in kharis is restored by fostering more kharis.

Sin is an important concept, but it is unrelated to Hellenismos. One should never feel guilt for doing wrong by the Gods--only, perhaps, sadness for not doing right. Sin and guilt have no place in our religion, although they have a place in many of us as our Western societies are often drenched with Christian values and morals. It's important to untangle yourself from these subconcious influences to live an authentic Hellenistic life, which is not better than an Abrahamic one, only different. And the differences count.