What is a min (heretic)? And how does one become a min?
And what are the Halachic Ramification about a min? Some Examples: Can't talk to a min. No matter what reject min's teshuva. etc.
(Some help tagging)
There are many instances where this is discussed, so for simplicity's sake I'll just quote a few passages from the Rambam.
The Rambam defines the terms 'min', 'apikores', and 'kofer' in Hilchos Teshuva 3:6-8
In addition, while it isn't listed here, the Rambam also requires that one believe in Divine retribution in order to not be considered a heretic of some kind (Commentary to the Mishna, intro to Sanhedrin 10:1)
Regarding practical ramificatins, there seems to be no difference between a 'min', a 'kofer', and an 'apikores' - all of them lose their share in the world to come, and are in general excluded from being considered a part of the Jewish people (Source: Rambam Hilchos Avodah Zarah 2:5) Therefore, any law that requires a Jew, such as returing their lost object (Hilchos Gezailah V'aveida 11:2), writing of Sifrei Kodesh (Yesodei HaTorah 6:8, Tefillin 1:13), or testifying in court (Eidus 11:10) cannot be done by any of these categories of people, who from now on I will refer to as heretics.
In addition, one is not allowed to speak to such people, or respond to their claims (Hilchos Avodah Zara 2:5). In fact, the Rambam writes, based on the Gemara (Avodah Zara daf 26) there is a 'great thing' to kill them, either publically, if the socio-political climate will allow such things, or privately arrange for his death (Hilchos Rotzeach 4:10). However, the Chazon Ish (Yoreh Deah, Hilchos Shechita 2:16) wrote that this last halakha is not applicable today, and many great poskim have followed his view. (To clarify, I am NOT advocating the murder of anyone, just quoting the Rambam)
However, a person of such status can still do teshuvah (Rambam Hil. Teshuva 3:14)
I am uncertain which category Elisha ben Avuya would fit into based on the categories that Ramba"m mentioned (see linked article for the other category details.) My understanding of the Gemarrah is that they call him a "min". But based on Ramba"m's categories, it seems that he would fit more as a "kopher BaTorah".