I have a vague idea of what a Neder (an oath affecting an object's status) and a Shevuah (an oath affecting oneself) are based on cursory study of the Talmud, but what are the other 5 or so types of oath on the list?
The terms used in Kol Nidrei are:
Neder - a vow affecting an object (usually forbidding it in some way) or a vow to upkeep the Temple or gift to the altar.
Issar - a vow that forbids or prohibits something. (Ex. "This loaf of bread is assur to me.") The Hebrew "Issar" means to bind or restrict. It can be a neder or shevuah etc. as long as it forbids.
Shevuah - an oath declaring one will or will not perform an action.
Cherem - a ban (usually against benefitting from a person or forbidding your own benefit to others) or a term used for a donation to the Temple.
Konem - a Talmudic nickname for Korban (Temple offering upon the altar)
Kones - another Talmudic nickname for Korban
Kinui - "nickname" , meaning any substitute term for a vow or a comparative word linked to a vow (like the above konem and kones).
(See Talmud Tractate Nedarim 2a with the explanation of the Ran on the 1st Mishnah there; and the Mishnah on 10a.)
To add to David Kenner's answer, one of the fundamental principles in the laws of Nedarim (vows) is that any kinui of a neder is equivalent to the neder itself. That is, any shorthand or slang that people use in place of the word has equal force, following the principle that in vows we follow ordinary language, not any prescribed formulation (Nedarim 49a).
The words "konam" and "konas" are kinuis for "korban" - sacrifice. That is, saying "this apple is a korban to me" (or a "konam" or a "konas") is the equivalent of saying "this is as forbidden to me as the property of the Temple".
Thus the term "kinui" is the archetype of some of the others. It comes at the end to include any other kinui not covered in the text. On all of them, we repent and wish them to be void.