Can an Orthodox Christian of one diocese receive sacraments at a coterminous one, e.g. a Greek Orthodox at an OCA parish? I'm presently a confirmed Catholic but am considering conversion to the Orthodoxy. Something I understand of it is that there is no single diocese in America, but multiple overlapping ones for historical ethnic reasons. In my city, there are several OCA parishes, a few Russian Orthodox, a Serbian Orthodox, and the largest is the single Greek Orthodox.

Something I have become used to as a Catholic is that I can attend Mass at any Catholic church and make confession at any Catholic church; this allows me to be a regular parishioner at a small parish but avoid confessing to a priest with whom I have a rapport by going to the cathedral which has a random priest in the confessional daily.

Within the Catholic Church, I've learned, it is allowed for a Roman to receive Eastern Catholic sacraments despite the distinct jurisdictions, but I feel as though this is partly because they're all under the same hierarchy.

Would it be permissible, then, for an OCA parishioner to make confession at the Greek church, or a Serbian to confess at a Russian church, without having to change his affiliation to that diocese?
The short answer is yes. I converted into an OCA parish. When i had to move, the closest Orthodox parish was an Antiochian one. On occasion, I have also attended srevices in a Greek parish. The important thing for me was to establish a Parish as my home parish.