Question: How should I dispose of my old sechach, lulav and esrog?
Answer: Although following Sukkos, sechach and arba minim are no longer mitzva objects and no longer considered to be kodesh (holy) they must still be treated with respect. Thus, while they do not require geniza (burying) they should not be thrown into a regular bin.
The Mishna Berura (21:6; 638:24; Shaar Hatziyun 664:20) writes that one should be careful not to leave one’s sechach or arba minim around on the floor after Sukkos where others may trample on it. Rather, one should recycle them with other branches, etc. or wrap them before disposing of them. Ideally, one should even treat the sukkah walls respectfully. Likewise, the Aruch Hashulchan (OC 638:12) writes that one should be particular not to abuse one’s sechach after Sukkos.
Once something has been used for a mitzva it is ideal to use it for another mitzva. The Shulchan Aruch (OC 297:4) writes that it is ideal to use one’s old hadassim for besamim (in havdala). Many Sefardim follow the Kaf Hachaim (OC 445:15; 664:60) who writes that the esrog should be made into jam and eaten on Tu Bishvat. One should keep one’s lulav at home (as ‘protection’) until erev Pesach, whereupon half is burned with the chametz (see Mishna Berura 445:7) and half to bake matza (see Rema OC 664:9).While some throw their used hoshanos on top of the aron hakodesh for Kabbalistic reasons, others have decried the practice (See Rivevos Ephraim 8:287; Nitei Gavriel Sukkos 79:7). One certainly mustn’t do so in a Shul where this isn't practised.