In my mind the true "hard part" would be in migrating business logic that lives in Oracle stored procedures (PL-SQL). Are there any tools that do a decent job in translating procs to non-Oracle dialects?
One of the main selling points of EnterpriseDB (built on top of and supporting development of Postgres) is a significant degree of Oracle compatibility, including PL/SQL, client interfaces, etc., so if you go that route you might not need much translation.