Some beings can't use Gateways, because they are not natural lifeforms.

It's been theorized that passing through a gateway involve a manipulation of reality/the pattern, and that not only the gateway itsef is such a manipulation, but passing through it manipulates yourself as well... you cease to exist on one side to exist somewhere else in the Pattern. The reasonning would be that the Wheel is unable to perform or register that "twisting" when the being who pass a gateway isn't natural. In short, the Wheel doesn't have "the data" to twist a Trolloc, or a Nym. Nym have human souls. Trolloc have animals (so we guess). When a Trolloc pass a gateway, the Wheel deals with it as if it was a wolf, or goat or falcon... but it isn't, and it dies in the process. That's a theory anyway, what RJ said is just that constructs can't Travel because they aren't natural beings - and left it at that.

Logically, this should be true for all constructs, including Gholam (which RJ confirmed was a construct...). Ogier aren't included - RJ specified they can Travel and they are natural beings, just of another race. Same for the Finns.

(on a side note... perhaps we will soon discover if Grolms, Raken etc. are natural beings from an IF world, or if they were constructs made in those if worlds.... The Seanchan could theorically lose all they menagerie if they attempt to make them Travel (though most are too big anyway for the sort of Gateways the damane will be able to weave).

Grey Men are humans. They are an unknown. Perhaps the fact their soul is apart from their body would make it impossible for them to use Gateways, and perhaps it has absolutely no ill effect.

Slayer is another unknown. We don't really know what he is - does what was done to him make the resulting being technically a construct or not? We know he has two souls, and special powers/abilities. He may not be "natural" enough anymore, or perhaps he is. Perhaps if he tried to Travel as Luc, he would die, as the Wheel considers this soul as not incarnated, and perhaps if he does so as Isam nothing bad happens, or perhaps the presence of Luc's soul in there would mess it up and he'd come out dead on the other side.

It's been theorized that since the True Power tears a hole in the Pattern, using such gateways doesn't involve a manipulation, and Shadowspawn and other constructs can use them. But it's unproven for now. Graendal probably didn't have a great enough access to the TP to make gateways, and her pawns used Portal Stones,so it proves nothing.