We have three toms. 1 bourbon red 1 Narragansett and 1 sweet grass. We have only four hens. 1 Bourbon red 1 Narragansett 1 sweet grass and 1 gray. We don't care if they mix and the kids are excited what crosses will come up!
By gray, do you mean a purebred Oregon Gray, which is quite rare, or do you mean the color gray. If just the color gray, it might be a mixed breed, or it might be a Blue Slate, Self Blue, Lilac, Bronze, or several others, depending on how your eye interprets colors. Can you post a picture?
As far as what colors will come up, you've got quite a lot of possibilities with this group. Here is a link to the feather color genetics page from Porter's Turkeys:
http://www.porterturkeys.com/feathercolorgenetics.htm. That can help you figure out what each potential cross would produce (a great learning experience for the kids, depending on their ages), but you've got the potential for more than a dozen genotypes (the internal genetic makeup, which may or may not be expressed in an animal's appearance), and probably just a few less phenotypes (the outward appearance of color or other features). If you're familiar with genetics, this page will give you everything you need to know to predict your possible genotypes. For the mixed breed birds, it can sometimes be difficult to determine what a particular genotype will look like. You can find many examples when you go through the Porter's website. If you're still stumped, I have heard that there is a turkey genetics thread on BYC that can answer questions.
If everyone is kept together in the same pen or yard, be careful that the boys don't fight on top of the girls when they squat down for breeding. That many boys with only that many girls might cause an issue, depending on the social relationships between them. The hens could easily be injured, or the toms might fight often enough or aggressively enough to cause injury. There are several posts on this thread of toms dying after prolonged fights, sometimes days after the event. If you keep them penned, consider that you may have build more pens to divide them up as breeding season progresses, probably one pen for each tom. If they all free range together, you may need to put a divider or two in their yard to prevent injury. There's no magic ratio, as I've seen anything from one tom to five hens up to one tom per 20 hens published as the ideal ratio for breeding pens. Most people have less hens per tom and do fine. But with three toms and only four hens, it's not just the very tom-heavy ratio you have to worry about, but the interaction between the three toms. I have 2 toms and 5 hens, and 99% of the time everything is perfect, as the toms are best friends and have a well established dominance between the two of them. But on rare occasion the submissive tom tries to breed with the dominant tom's favorite hen, and it gets really ugly around here. I can't imagine the chaos if there was a third tom in the mix, and one less hen. If you keep roosters in with the turkeys, I have found that some bratty little roosters tend to be instigators of fights, which can end up with two toms fighting each other long after the roosters have left the scene, so be careful of that if you have a mixed group.
Good luck with your turkeys. They're wonderful birds.