Saitama source of income during the three years Saitama was training and even before, he was unemployed, so from where did he get the money to "survive" ?
From bounties.

Certain villains have a bounty on their heads and Saitama survived by defeating those villains. See OVA episode Road to Hero.

(Contains spoilers if you haven't seen the episode.)
http://onepunchman.wikia.com/wiki/OVA_0