に当(あ)たってWhen, When doing something, On the occasion, At the time

Both mark the timing of an event. にあたり・にあたって emphasizes necessary preparations or intentions beforehand, as in 開発にあたり調査を行った (Before development, we conducted research). に際して marks the occasion itself, especially significant or ceremonial ones, as in 入学に際して祝辞を述べる (Give a congratulatory speech on the occasion of enrollment).

Both are formal expressions where one condition influences another, but with different nuance. につき means on account of or due to, as in 雨天につき中止になる (Cancelled due to rain). にあたり・にあたって means on the occasion of or at the time of, as in 退職にあたり一言挨拶をする (Say a few words on the occasion of retiring).

にあたり・にあたって is used for important occasions that involve preparation or intention, as in 出発にあたり挨拶をした (I gave a greeting on the occasion of departure). 際に simply means when or at the time of, describing something that happens concurrently, as in 出発の際に見送ってくれた (They saw me off at the time of departure).

Both derive from 当たる, but are used in different ways. に当たる means 'corresponds to' and functions as an indirect way of saying 'is', e.g. '父親に当たる人' ('a person who is [lit. corresponds to] their father'). にあたり・にあたって follows nouns or verb phrases and means 'when' or 'on the occasion of', e.g. '就職に当たり' ('on the occasion of getting a job'). Note that に当たる can also appear as に当たり in formal conjunctive form.

Both connect actions to a larger context, but with different emphasis. ついでに expresses performing a second action while it's convenient, e.g. '買い物のついでに郵便局に寄った' ('I stopped at the post office while shopping'). にあたり・にあたって is more formal and used for actions on a certain occasion, e.g. '開会にあたり、ご挨拶申し上げます' ('On the occasion of the opening, I extend my greetings').