Generally speaking, you would join an URNU in your first year (of a 3 year degree) as they usually "recruit" 17 undergrads per year. Some URNU's offer honourary membership, were you attend un-uniformed, pending enrollment if someone decides to leave. Priority is given to first years for the simple reason they are likelly to attend for the full 3 years.
If there's a place arising because someone has left, then you may join in year 2 or 3. Medical students often join in year 3 of their 5 years. Occasionally postgrads join, if there's a spare place.
Depending on the URNU, sometimes up to 100 people apply for the 17 places.
Pretty much as Ninja said, priority to the first years and any second years who meet the specification, or whatever it may be, get places. Competition can mean there are around 3:1 people/place applying, though sometimes the entry can be expanded to around 19 maximum, depending on your unit. Associate membership is also offered as well.
As for 3rd years, generally I don't know, seeing as I got raised eyebrows from the board (the CO and a senior officer) initially as they thought I was a 3rd year until I corrected them.
Hope this is some help, though probably best to speak to the URNU concerned,