A new offer of contract that terminates the original offer is

A counter offer is a new offer made in response to an original offer, usually changing one or more of its terms, such as the price or quantity. Making a counter offer automatically cancels or terminates the original offer, because it is treated in law as a rejection of that offer combined with a fresh proposal of the counter offer's own terms. The original offeror is no longer bound by their first offer once a counter offer has been made; they must decide whether to accept the new terms instead.

The other terms do not describe this situation. An invalid offer is one that fails to meet the legal requirements of a valid offer from the start, rather than one terminated by a later response. A void contract is an agreement that has no legal effect at all, which is a different concept from an offer being replaced before any contract is even formed. A quasi contract is an obligation the law imposes even though no real contract exists, again unrelated to the process of offer and counter offer.

Examination reminder: remember that a counter offer does two things at once: it kills the original offer and creates a brand new one that the original offeror can accept or reject.