Not only can kohanim consume terumah, but they may feed it to their wives, their daughters, their Canaanite slaves and their livestock (cf: Rambam, Hilkhot Terumot 6:1 and 3). So far as their own consumption is concerned, kohanim may not consume terumah unless they are in a state of ritual purity (so, for example, Berakhot 2a: בשעה שהכהנים נכנסים לאכול בתרומתן, etc). That being said, what about the people they are feeding?
• Does the wife of a kohen need to be ritually pure? (This is not mentioned as one of the differences between kohanim and their wives in Mishna Sotah 3:7, so I would have assumed that she does);
• Does the daughter of a kohen need to be ritually pure? (That the rules concerning one's daughter may be different from those concerning his wife is borne out by the principle that a man's wife is an extension of his body but his daughter is not; אשתו כגופו, Yevamot 62b - used in this context by Tosafot, Ketubot 52a, s.v. והיו מבקשין);
• Does the Canaanite slave of a kohen need to be ritually pure? (I may have thought not, given that the laws of ritually purity are laws that only Jews must abide by, but Tosefta Zavim 2:1 seems to imply that they might);
• Are there limitations on what type of livestock may consume terumah, or on the physical condition of the livestock? Does it need to be a kosher domesticated animal? May it possess blemishes that would otherwise invalidate it from being ritually consumed?