Do sukkah decorations need to be discarded in a specific way? What about used glasses that held oil for shabbos candles? the wicks?
Articles that were used, but are no longer being used for the mitzva, such as old worn out tzitzis, are called tashmishei mitzvah. The general rule with tashmishei mitzva is that it does not have to be put into shaimos like seforim, however it should not be thrown out or used in an embarrassing way, i.e. in the garbage, but it can be put in a place that it will decompose or disintegrate on its own. Items that weren’t used for the mitzva itself, but were used to help the mitzva, such as candlesticks, the glasses used to hold the oil of the menorah a tallis bag, are called tashimish d’tashmish. These items may be thrown in the garbage, see sources.
Regarding succah decorations, they may be put into a bag and thrown out, see Ginzei Hakodesh in the garbage 18-11 in the name of R’ N. Karelitz zt”l.
The glasses that held the oil are considered tashimish d’tashmish and may be thrown out however there is preference to wrap them up before throwing them out. See Ginzei Hakodesh 19-13,14. The leftover wicks however would be considered tahmishei mitzvah, and would be like the tzitzis strings. See Ginzei Hakodesh 19-12.
O:CH 21-1, M:B 21-6. Regarding tashmish d’tashmish see Ginzei hakodesh 16-10, in the name of R’ Vosner, R’ N. Karelitz zt”l, that it may be thrown out. He does however bring from R’ Eliyashiv zt”l that if it is evident that it was used for a mitzva, such as a tallis bag, then it shouldn’t be thrown out in an embarrassing way. However if it is difficult, it may be wrapped up and put in the garbage.