Writer handles the Unicode character repertoire. As far as I know, unusual ligatures like AV, AU or AR are not defined in Unicode. Consequently, if you already found AV, this is a specific extension in a font (you didn’t mention it either). Such “private” ligatures are managed by the font renderer which makes use of dedicated internal tables in the font file.
AE and OE are not defined as ligatures by Unicode, though they look like ligatures. AutoCorrect may convert a sequence of A E or O E (and their lowercase counterparts) into Æ or Œ but this is not compulsory (and may change meaning in some languages).
The only Latin Unicode ligatures are in the Alphabetic Presentation Forms block starting at U+FB00. They are ff, fi, fl, ffi, ffl, ft and st.
This does not mean that a font provider can’t add other special purpose ligatures, but they are then enabled through the font features subdialog in Writer.