Is there anywhere in Street Grimoire that says that regular mages cannot learn toxic spells or that an adept who does not follow a toxic path cannot use the Radiation Elemental Weapon power? It seems to me that they could, I just wanted to make sure.
By regular mage, I assume you mean a mage that does not follow a toxic tradition. On pg. 87 of Street Grimoire, the paragraph below the Twisted Arts header says (emphasis mine):
Toxic magicians, exclusively, may learn the spells Pollutant Stream, Pollutant Wave (p. 106), Radiation Beam, and Radiation Burst (p. 105). They may also learn the toxic metamagics of Corruption and Taint (p. 87) and can learn and perform the ritual of Leeching (p. 133). Toxic adepts, exclusively, may learn the Toxic Strike power (p. 176) and the Plague Cloud power (p. 173).
This would forbid one not on a toxic tradition/path from learning those spells/metamagics/powers.