From the scholia to Homer, Iliad 18.292, where the headword is used (of Zeus); it is the third person singular, aorist, of the epic/poetic verb o)du/ssomai or o)dui/omai (LSJ entry at web address 1). Hesychius omega65 gives more synonyms along the same lines.
This verb was seen as the origin of the name Odysseus. The pun appears at Odyssey 1.62 (web address 2); 5.340, 423; 16.145-7; 19.275, 407-9; see also Sophocles fr. 880 Nauck (= 965 Pearson).