They are all essentially the same, and work as translations both of "the past" and "his/her past" etc.
La estinteco is "that which was." It forms part of the triad:
estinteco — estanteco — estonteco
that which was — that which is — that which shall be
La pasinteco is "that which has passed."
pasinteco — nuno — venonteco
that which has passed — the now — that which shall come
La paseo is an alternative term for the past. It comes (I think) from the Parnasa Gvidlibro (1932), which suggested many new words. It is very frequent in literary Esperanto. Otherwise it is used as the name of the grammatical tense (along with prezenco and futuro). Your use of it depends mostly on your attitude towards literary neologisms. Note however that it has the advantage that it avoids blurring the meaning of -eco.