ORM-style server-side programming languages (OO replacement for PL/SQL?)
Oracle has Java server-side, but I'd caution that it is not a replacement for PL/SQL. There is no better language than PL/SQL for manipulating data stored in the database - Java may be appropriate for computationally intensive business logic.

For postgres,


  There are currently four procedural languages available in the standard PostgreSQL distribution: PL/pgSQL (Chapter 39), PL/Tcl (Chapter 40), PL/Perl (Chapter 41), and PL/Python (Chapter 42). There are additional procedural languages available that are not included in the core distribution


But I think it is fair to say that PL/pgSQL is the most mature and feature complete (and, you may be sorry to hear, very similar to PL/SQL).

I don't know much about MySQL stored procedures but here is a link to the docs