Tsinnorit and oleh always appear as part of a pair. Tsinnorit is always paired with either merkha or mahapakh. Oleh is always paired with yored. (Yored looks the same as merkha, although their roles quite different.) These partner accents (merkha, mahapakh, and yored) behave like normal accents, which among other things means they never appear on an initial vocal shewa.
Because oleh is always paired with yored, in many contexts it is useful to think of them as forming a single accent that happens to require two marks. This accent is called oleh veyored. Similarly, in many contexts it is useful to think of the tsinnorit pairs as merkha metsunneret and mahapakh metsunneret, although these names are not widely used. Note that these are all somewhat analogous to the two-mark accent revia mugrash, especially in editions where the revia of revia mugrash is always explicit.
Yored never appears without oleh, but merkha and mahapakh can appear without tsinnorit.
Neither tsinnorit nor oleh is ever the primary accent on its word. Yored is always the primary accent on its word, but the partners of tsinnorit may or may not be the primary accent on their words.
Oleh usually appears before yored but, rarely, can appear on the same letter as yored.
Tsinnorit always appears before its partner.