They are very similar. It is more common to see certain phrases used. For example, "He was leery of giving out his email address." "He was wary when approached by beggars." "When speaking with strangers, he always had a guarded expression." People usually say "leery of" some situation or danger. "Wary" can be used the same way, like being "wary of" some situation. But, you could say that a person was wary, as a description of the person, and you usually would not use "leery" in that way. "Guarded" can be used to describe the way a person acts, but it can also be used to describe their expression. "Wary" can also be used to describe an expression. "He looked wary." or "She was guarded." Wary is a little more like suspicious, while guarded is a little more like careful, and leery is a little more like nervous.

They all mean very similar things although I must confess that leery is not a word that I use or hear others use. 'wary' normally means that one does not trust someone or a situation. 'He is wary of walking the streets in the dark.' 'Guarded' can mean that someone is not very open about themselves for fear of being hurt. 'With new people, he was very guarded'.