Well it triggers on Sonic and Cold spells, so....Sonic and Cold spells
So that includes all the Sonic and Cold Epic Strikes (Fatesinger, Draconic, Magus, Primal). Burst of Glacial Wrath should too. Does not include Fey or Carceri Warlock blasts, though.
As for cross-class spells...Stormsinger is still a caster, so you really dont want to multiclass too much, ideally not at all. Being able to proc lightning a little more often is not worth giving up caster levels on your actual main spell rotation.