yes and no
The meaning might be the same, but the association, style, intention... make only first one true to the point.
"Waste" has a larger scope of meaning than "throwing away" which is meant in all three sentences.
In careless speech yes, they will pass about the same message, but in careful writing probably no - only first one is precise.
For example:
1. "waste" might associate to "recycle" so "we'll just waste it" has one possible association that is not the one you wish for here.
2. Other sentence "we'll just waste it" is too complex construction, futur + passiv + 'just', for something that is in essence an order or pledge "eat that [damn] chicken", which is underlined. "we'll just waste it" suggest that we are deciding about the food, but actually we do not, in truth this is what we are sorry about: it is that we can't do anything else but to throw the rest of the food away. So there is no real action from our part, and then "we will just..." does not fit too well, unless you feel no remorse for throwing it away, rather formally state the result of "not eating that last piece of chicken", which is to say that the third sentence does not suggest anything to the eater. First two do: "eat it" or "we will have to" or "we will have no option but to". Actually I would use the third one if I would like to say "you do not have to eat it".
3. "it will just be wasted" means - it will not serve its purpose. One of the reasons could be that nobody else would eat it later. This does not explicitly say that we will throw it away. Wasted = won't be used. So we are sorry, for example, why we have spent any time preparing it.
"it will just go to waste" says a little bit more and a little bit different: we are not sorry, we say a strict consequence, for example, here we do not suggest that the time we spent preparing it was wasted as we do with "it will just be wasted"
So, no, with all details encountered, they are not the same.
A.
it will just go to waste
we say that the food will be otherwise thrown away
B.
it will just be wasted
we suggest the eater to finish his meal so the preparation (among else) would have a higher efficiency
C.
we'll just waste it
implies what we have decided to do if the meal is not completed, but no more than that
A and C are different in it that A says about an independent and enforced action and C about a conscious decision.