Strictly speaking, מעוז צור is a song themed on Exile and Redemption; though it has, in this regard, nothing more to do with חנוכה than it has to do with פסח, בין המצרים, פורים or משיח, it is nonetheless (almost) universally sung on חנוכה (though it can be sung at any other appropriate occasion - I just am not aware that it ever is). This song is a special highlight of חנוכה at Breuer's, itself a unique experience of its own.
[JC - Mombach arrangement] מעוז צור 1
traditional German arrangement - מעוז צור 2
[JC, instrumental] traditional German arrangement - מעוז צור 3
[JC, arranged BM] Italy - מעוז צור 4
[JC, arranged BM; instrumental] Italy - מעוז צור 5
[JC] Slonim - מעוז צור 6
[composed Nissan Yust] Vizhnitz - מעוז צור 7
[FS] an adaptation of the original German melody to Maqam Ajam - מעוז צור 8
[LSC] מעוז צור 9
[AAC, HB] מעוז צור 10
[DK] Morocco - מעוז צור 11
Often various melodies are set just to the stanza that deals with חנוכה specifically:
יוונים 1 - Boyan