Can I claim right to possession when the sheriff comes to lock out the named tenants?

The sheriff deputies will probably tell you that is an issue you have to take up with the landlord by suing him for unlawful eviction, but they no idea whether you are legally entitled to be there or not. They have a very limited role to play and will not get involved in any disputes if they can avoid it. Whether you have any case against the landlord is questionable. Did the landlord know you lived there; if he did not, how was he supposed to serve you? It is standard procedure to ask for relief against anyone not on the lease who lives there without serving them. When parents are evicted, their children get evicted to. If you claim you have a right to live there, then you also are liable for the back rent and could be sued by the landlord, which might prevent you from successfully renting another premise.

You need to file an answer in the case if 10 days has not passed. If you're too late you need to claim a right of possession via an ex parte motion in front of a judge before the Sheriff shows up or you will be tossed out.