Shrive and oil
Offended that the old woman would slight him in favor of a medical student confidently declaiming about "rotten teeth and rotten guts," Stephen imagines Mulligan performing socially esteemed rites analogous to those of churchmen. Prompted perhaps by Mulligan's ongoing impersonation of a priest and his mention of "the dissectingroom," he thinks of the "voice that will shrive and oil for the grave all there is of her but her woman's unclean loins." Like doctors, priests attend the dying, preparing their parishioners for holy burial.
Thornton cites an article by Willis E. McNelly, “Liturgical Deviations in Ulysses,” JJQ 2 (1965): 291-98, on the Catholic sacrament of extreme unction, in which the priest comforts the dying by anointing with olive oil “the eyes, the ears, the nostrils, the mouth, the hand, the feet, and the loins. Yet the annointing [sic] of the feet may be omitted for any good reason, and the unction of the loins is always to be omitted if the subject is a woman” (297).
As in most liturgical and theological matters, Stephen is well versed in the arcane particulars of extreme unction. "All there is of" the old woman will be oiled for the grave except her genitals, those "unclean loins" that Stephen has not yet managed to secularize.