Well, my etiquette books are at home, so I hope my memory serves:

Senior and Junior designations properly apply to a parent and child with identical names, and only while both are still living. Upon the death of one, the need for and appropriateness of addressing one as a senior or junior also dies.

First, second, third, fourth designations apply to multiple people with the same names, but not necessarily in direct lines of descent, and the numbers are assigned by birth order. In Flatlander's case, it seems that his father is Eustice John Flatlander I, his cousin is Eustice John Flatlander II, and he is Eustice John Flatlander III. As I recall (and I am not sure on this, and will have to check), the I/II/III designations do not change with the death of any in the line.