These three determiners do not have the same function, and cannot be used interchangeably. In other words: they do not "mean" the same thing.
Each
"Each" allows the speaker to focus his/her perspective on the details, on every specific singularity, and has a dissociative function (i.e. you consider each element separately and individually). Example: "Each bird in the cage had a different plumage" (here, you look at each bird individually, and notice the unique details about each of them). For this very reason (of uniqueness), "each" can only be followed by a singular noun. "Each bird" is correct but "each birdS" is wrong. You may write "each bird in the cage looked the same" but it still means that you took the time to consider them individually before coming to that conclusion (so the function of "each" is to isolate and individuate the elements of a series).
Every
"Every", on the contrary, is used to synthetize, globalize, and uniformize.
Example: "Every bird in the cage looked the same to me" (the speaker did not take any time to consider them individually, otherwise s/he would have noticed the differences in hue). With "every", the diverse elements of the list are generalized into a broader class or category. It is therefore the contrary of uniqueness. It is generality. "Every" is also followed by a singular (no every birdS), but only because it is a broad category, as in "everybody" (i.e. the regular type of person, in general). Because it is used for generalization, it would make no sense to write "every bird in the cage had a different plumage".But you may write "every bird had the same plumage".
All
With "all", you insist more on the notion of plurality, of a unified whole.
Example: "All (of) the birds in the cage had blue feathers" (you consider a mass of blue feathers). When followed by a noun, "all" is always followed by a plural (« tout homme » : all man every man or all men). When it is used as a general pronoun, it is followed by the singular when it means "everything", as in "all is lost", or by a plural when it means "all people", as in "all have sinned".
A TIP: If you can insert "particular" or "in particular" in your sentence, then you should use "each". If you can insert "generally" in your sentence, then you should use "every".
