Sorry, I didn't finish my thought with Greer... DH was talking to me as I was typing that response. Sorry! To me, Greer isn't girly at all... it's the opposite. I've known quite a few Greers, and all have been farmers and extremely rough around the edges. Although I don't think it's a bad name, I think of a guy spitting tobacco juice on the floor... It doesn't match Troy and Rex quite as well to me, as Troy and Rex are extremely manly, but also slightly more refined due to the connection with Classical civilizations.
Your username is "mylittleking".... Why don't you choose Ryan (it means little king) ;)
Rex, Troy &
Adler - I like it, but it feels a bit last-namey to me, and doesn't fit in well with your sibset at all. Alder is another I like (perhaps even more than Adler), but it also doesn't work with Rex and Troy.
Ajax - I don't like it. I mean, it is short and strong like Rex and Troy, but it just has something about it that doesn't feel right. Maybe it's just the cleaner that makes me think that?
Archer - This name has grown on me a lot recently (I don't like the NN Archie though, Arch would be a cool one). I think it fits in quite well with your sibset. It's short (sounding) and straight to the point (pun intended). It's growing popularity is something to reflect on, whether that bothers you or not. With this name, I personally wouldn't let that effect my decision too much.
Braun - I don't like it. Too 'brawny'.
Chester (nn Chet) - It's alright, nma, but alright.
Conrad - I like this name a lot a lot. It's much longer than Rex and Troy, but it does have the same sort of strong, no-nonsense feel to it. I think it'd be a great option.
Crew - I don't like it. Seems like the word 'gang' to me.
Eric - Normally I'd be pretty mediocre about this name, but with Rex and Troy, Eric just fits perfectly. It's strong, it's short, it's well known but not overly common. It's the exact same kind of name as R & T.
Greer - I don't like it much.
Miles/Milo - If this one keeps coming back to your list, keep it there. It's a different feel that R & T, but you don't need to make a perfect sib-set, each kid is their own person. And Miles and Milo are great names (I prefer Miles)
Paris - Yeah... no.
Victor is also really growing on me for you. And Dean is loosing some steam for me, I don't like it with your last name. Bram is potentially cool. Wade I don't like.
My overall favorites for you now are Victor, Eric, Conrad, Archer and Miles.