The "Crank That" rap star is suing over comments he claims were made on Tasha K's "Unwine With Tasha K" podcast about William and the rapper being in a romantic relationship ... which Soulja claims are nothing but big, fat lies.

According to the lawsuit, William told Tasha on the podcast in May that he and Soulja Boy were lovers in graphic detail ... and the clip went viral online.

Soulja says he gave both Tasha and William a chance to right their wrongs by sending them a retraction letter around the time he made his social media posts denying the allegations.

But now Soulja's upping the ante ... suing the pair for defamation, sexual harassment, violation of right to privacy, intentional infliction of emotional distress, and more.

William, for his part, later doubled down and tattooed Soulja's name on his cheek -- in purple ink, no less.