You've got a lot of feather color genes in any of those mixes and you've got a barred mixed rooster....which means all chicks, male and female, will be barred (white head dot).
So there is really no way of knowing what the parentage is of this chick nor if it is female or male.
As to egg color.
If the Delaware or SS hen is the mother, then you have 50% chance that it will lay a blue or green egg, assuming dad as an EE/Barred mix got one blue shell gene. (He might not have...which means you get 100% brown).
If an EE hen is the mother, and she has the blue shell gene (did the chick hatch from a blue egg?), then you will have 25% chance of brown and 75% of blue/green (see math below).
You can have a maximum of 2 genes for blue shells. Pure breed blue layers, such as Ameraucanas and Cream Leghorns, carry both blue genes...so have 2 blue genes.
Each parent gives 1 blue (or non-blue) gene to the offspring. It is a crap shoot as to which of the genes the parent passes down. (Which is why you want 2 blue genes in a parent to assure blue passing down.)
The nice thing is, as blue is dominant, you only need 1 blue gene to be passed down to get a pullet that lays a shade of blue.
So the math sets in.
If both parents have 2 blue genes, then all offspring will be blue layers.
If 1 parent has 1 blue gene, the other 2 genes....all offspring will be blue layers, varying shades.
If 1 parent has 1 blue gene and the other 1 blue gene (your EE mixes mated), then mathematically it works out to be 25% non-blue and 75% blue.
Green is formed as brown wash (from brown layers) is applied over the blue shell base. It takes about 13 genes for brown wash, which can be in varying degrees. Brown over white produces brown eggs. Brown over blue produces green eggs.
SS lay a tinted egg and so do Delaware, so you will have a light green egg if the pullet received blue genes. It may be a brighter green if the pullet received a blue gene from mom and dad.
In order to get olive, you have to have a dark brown egg layer as one parent. The dark brown wash over blue produces the olive.
Good luck with your egg color project. It is a lot of fun breeding for a colorful egg basket.
LofMc