1) Mains transformer + rectifier
2) Battery + Vibrator + transformer. The Battery was often a wet-cell
lead-acid accumulator
3) HV battery
4) Transistorised oscillator + transformer (once transistors were in
common use)
I recall using two Dormeyer strobe units--one using a traditional
510v battery pack and the other using a lead-acid battery (encased in
stainless steel) and vibrator that also had a 115vac connector for a
line cord. Recycling time was slow with mains power and incredibly
slow with battery power.
I do remember the "miniature camera" 22.5v photoflash, but to my
knowledge, the standard "press photographer" flash units that used
large incandescent-lamp-sized bulbs all took D cells.
Cheers,
Chuck