If you put your house in an irrevocable trust, that means the trust owns the house. Period. "Irrevocable" means what it says"”can not be changed. Whether the house can be
sold by the trust depends on whether the trust document permits that or not. Even if the house can be sold, the proceeds must remain in the trust. Whether those proceeds can be used to buy a new house again depends on the terms of the trust.
I do not know why you are considering putting your house into an irrevocable trust. Generally, there is no reason to do this. You can put your house into a revocable living trust in order to avoid probate. Because that trust is revocable, you can remove the house from the trust at any time, and sell the house as you wish.
Be sure that you understand the drawbacks, and benefits if any, of putting your house into an irrevocable trust. Only if you decide that somehow, for you, there wold be substantial benefits that outweigh the drawbacks should you put your house into an irrevocable trust.