1 and 3 are good.
2 is no good.
"Any one of which is distinct" has the following problem.
If we want to say that all the objects in a set have some property, like distinctness, beauty, the color red, or whatever, then this is simply expressed using "all":
Any one of the flowers in this garden is beautiful.*
All of the flowers in this garden are beautiful.
The "any one" is possible, but is only used when all the objects have some property such that only one object shall be selected as a result of that property.
Any one of these parts is suitable for the repair job. [All are suitable, but only one is understood to be required for the repair job, which allows this grammar to be used.]
Note that this does not depend on the presence of "repair job", but on the semantics of the property of suitability:
Any one of these parts is of good quality.* [What? You mean all of them are of good quality.]
Any one of these parts is suitable. [Understood: suitability for some application that calls for one.]
Any two of these parts are suitable. [Clearly understood: for some application that requires two.]