I live at home with my aunty and about four months ago she has taken my property up to my nan's (without my permission) who lives across the state. Is it illegal for her to keep my possessions without my consent?
Yes, this is illegal. If by "across the state" you mean some distance away but in the same state then the exact law will depend on which state you are in, but as a rule any "conversion" of property to the use of another counts as theft. In this case your aunt has "converted" the property to the use of your Nan (funny legal phrase). The fact that the people doing this are your relatives makes no difference.
(When asking about the law here you should always say which state you are in.)
Although theft is a crime, you could also start a civil case to get your property back without involving the police. The details depend on where you are, but try googling "(your state) small claims court". Many states have a process for collecting low-value debts or other property without needing lawyers.
You need to have a firm conversation with your aunt about this. Tell her that you want your property back, and don't back down. Also call your Nan and explain this to her as well; she may not have realised that she is in possession of stolen property, which is usually a separate crime.
If you want more advice on how to get your property back without starting a family row then you might ask on the Interpersonal Skills SE, but it might be better to start with "When are you planning to return my property?" and leave "You are a thief" as a last resort.
Edit: As Eric Nolan points out in the comments, you may be a minor. If you are under 18 then your aunt has authority over you that she wouldn't have if you were older. For instance, if she is concerned about your use of video games impacting school-work then confiscating your console and putting it out of your reach would be perfectly legal.
In order to prove theft beyond a reasonable doubt, it would be necessary to prove that you could not plausibly have consented to her taking of the property, nor performed any action that might reasonably have been construed as consent. If she claimed that you gave either specific verbal consent to her borrowing the item or general verbal consent to borrowing some kinds of items, she made no attempt to conceal her actions, and she was willing to return the property on demand, a court would likely side with her on a he-said she/said, given the possibility that both you and her could be telling the truth, but she had misunderstood your intentions.
On the other hand, if you demand the item back, and it is sufficiently valuable as to be implausible as a gift, then even if she claimed you'd verbally given (as opposed to lent) it to her, a court would be likely to side with your wanting the item back. Even the court believed that you had said something which she misconstrued as making a gift, the fact that she misconstrued your intentions would not justify her being allowed to keep the object.
I suspect you're in the US so this wouldn't apply but interestingly, in France, theft between ascendants, descendants or spouses cannot be prosecuted (article 311-12 of the code pénal). In that case, your age, the intent to keep the property permanently or your ability to prove you didn't consent are all moot, it's simply impossible for parents or grand-parents to commit theft on their (grand-)children. Your aunt would not necessarily be off the hook as she wouldn't be covered by this provision.