たり〜たりする

ながら runs exactly two actions at once, under one subject. たり〜たり samples an open list whose members just take turns over time.

ことがある says one event happens now and then (遅おくれることがある). たり〜たり lists it as one example from a longer, unnamed list.

て fixes the order and presents the list as complete (食たべて寝ねた). たり〜たり samples an open, unordered list instead (食たべたり寝ねたりした).

たり〜たり samples an unordered set, so swapping the two changes nothing. ては〜ては fixes the order into a loop (書かいては消けし vs 消けしては書かき).

や lists nouns only (掃除そうじや洗濯せんたく). たり〜たり lists actions instead, and must end in する (掃除そうじしたり洗濯せんたくしたりする).

たり〜たり needs a final する to carry the sentence's tense. やら〜やら takes bare nouns, usually closing in で or の, colors the list unsettled.

行いったり samples "doing things like going." 行いったら sets a condition instead.

たり〜たり just lists two things you actually did, plainly (食たべたり飲のんだり). だの〜だの instead complains, listing things someone kept saying or doing.