Question: What are we to do with last years palms? with left over holy water? scapulars that have become dirtied? Rosaries beyond repair? What was the purpose of the lemon and bread slices at the Easter Vigil? What is done with last years Holy Oils? What is a sacrarium?
Answer: All of the questions deal with the proper disposal of Sacramentals after they have outlived their usefulness.
The "Sacramentals" are material things, blessed or consecrated by the Church through Her priests to focus the attention of the faithful on holy things. They are to be treated with respect and ought to be disposed of in a becoming manner. As it would be unseemly to put holy things out for collection with the trash, it is customary to burn those that can be burned and to bury those that can not. If you are unable to arrange for disposal, the parish priest may be able to do it for you. In fact, the ashes blessed on Ash Wednesday are the remains of the branches from last year's Palm Sunday.
The consecrated Oils of the Catechumens and of the Sick, and the Holy Chrism, are treated with special respect since they are the matter of several sacraments. At the Vigil, after handling the Oils, the priest cleanses his hands with the juice of the lemon, which is in turn absorbed by pieces of bread, which are later burned. Last years Oils (replaced by this years' -- consecrated by the bishop on Holy Thursday) are burned.
The sacrarium is a sink in the sacristy with a pipe that extends into a drain field in the ground (i.e. not the sewer). It receives the water from the small bowl used by the priest to wash tiny particles of the Blessed Sacrament from his fingers after distributing Communion outside Mass. In any case where the Blessed Sacrament becomes inedible, It is allowed to corrupt to the point where It no longer has the appearances of bread or wine and is washed down the sacrarium. The sacrarium may also be used for the disposal of last year's baptismal water following the blessing of new water at the Easter Vigil. Lacking a sacrarium, such things are disposed directly into the ground in a place where no one can walk upon them.