Taking OD to mean "drug overdose", it means his addiction to the (injected) drug got worse.
I don't see a specific reference to heroin, but it could be that, no doubt.
The "needle" refers to the hypodermic needle used for intravenous injection.
The use of "draw" (obj. + direction) is defined by its etymology here; a figurative use meaning "to attract".
(draw c. 1200, spelling alteration of Old English dragan "to drag, to draw")
(attract (v.) early 15c., from Latin attractus, past participle of attrahere "to draw, pull; to attract," from ad- "to" (see ad-) + trahere "draw" ). Similar to "tractor", "traction", etc.