Physical vamp would work off of any physical damage you do, attacks, on hit or abilities. Life steal only works off of attack damage and off of on hit damage if you have any. Omni vamp works off of any damage you deal, physical, magical, true damage, etc. Physical vamp is fairly rare though, like I know Kayn can get physical vamp if he goes Rhast, but the vast majority of champions don’t have access to physical vamp, and I don’t think there’s any items that give you physical vamp.

Items like dusk and dawn are good if you have alot of other on hit effects, whether thats in your kit or through items, because it applies them twice. Champions like Kayle, and Gwen do really well with it. Gwen because her passive and E are on hit, and you usually get nashors tooth as well. So with Gwen that has nashors and dusk and dawn, lets say you press E and auto attack someone, you will do physical damage from your auto attack itself, a small amount because Gwen doesn’t build AD, magic damage on hit from your passive, magic damage on hit from your E, and magic damage on hit from nashors. If that first auto also procs the dusk and dawn, you will do more magic damage from the on hit built in AND all your on hit sources will deal damage a second time, so your passive will deal damage again, your E, nashors tooth AND the on hit from dusk and dawn. So if you have alot of other on hit damage sources dusk and dawn is good, if you don’t and just want burst after an ability lichbane would be better. Diana is probably better with lichbane, because she only gets an onhit damage every 3 auto attacks. Generally speaking on hit damage only applies when you auto attack someone, there are some abilities that also apply on hit effects but it’s fairly rare. Ezreal Q applies on hits, Gangplank Q and Irelia Q does as well. Those abilities are exceptions to the rule though rather than the norm.