Thordan primarily makes use of ice and lightning based attacks, with a splash of fire that mostly comes from his knights/ meteor circles.
Alexander is usually a holy elemental summon and he uses that alongside his time theme/element in FFXIV.
As for Shinryu he replicates moves from each of the classic six primals at some point or another. I'd peg him as generally astral/ multiaspected to each element. Fitting for his rainbow scales.