Is my uncle and his family still considered guests who must be honored and served according to Sharia, given that their stay has lasted nearly two years, and they neither work nor respect the privacy of the household?

Hospitality in Islam is for three days; anything beyond that is considered charity. Therefore, your uncle and his family's prolonged stay is not permissible if it causes you embarrassment or inconvenience, especially with the presence of sons and daughters. You are not obligated to serve them after the three days. A guest is not permitted to prolong their stay with their host so as not to put them in an awkward position.

If there is a mature son among his children who is not a mahram to you through suckling, then cohabitation is not permissible unless the house has multiple separate rooms and entrances/exits, and there is no shared use of household utilities like the kitchen and bathroom.

Your uncle should be informed of this religious ruling gently and asked to leave.