Well, if everyone is lucky enough to actually get him to attend his own birthday party...
I could see him ripping apart the wrapping off his gifts and throwing anyone out of the room that gave him a present he didn't like.
I could see Izaya giving him a snake nut can.
That would lead to Shizuo going on an all out rampage. I could also see a fight going down where Izaya would want to give Shizuo "birthday punches." 
♫ They see me trollin', They ragin', Patrollin' and try'na catch me writin' derpy. ♫