The word vestry has two meanings that are more or less unrelated, though they have a common origin. A vestry is a room in which people put on vestments, or robes. A changing room. Since people typically do not take off their street clothes to put on vestments, a vestry room is not a private place but often rather more of an alcove.
A vestry can also be like a board of directors for a parish. In many provinces of the Anglican Communion, including those in North America, the business affairs of a parish are managed by a vestry that consists of members elected from the congregation.
"Vicar" has meaning similar to "rector." The difference between "vicar" and "rector" has to do with money. A vicar is the priest in charge of a parish or mission that is supported financially from the outside, while a rector is the priest in charge of a self-supporting church. In England most churches are supported by their diocese, so most of the priests in charge of English churches are vicars. In many other countries, notably the USA, most churches
A "Vicarage" is normally a house occupied by a clergyperson who usually (but not always) turns out to be a Vicar rather than a Rector.
A church warden is an appointed administrative position in a parish church. Usually one finds two wardens, called Junior Warden and Senior
Warden, or perhaps People's Warden and Rector's Warden. They have specific duties pertaining to the earthly operation of the parish.