Importing data from MS Access database to an existing Postgres database
I'd tend to export each table as CSV from Access, something it's quite good at. Then import it into PostgreSQL using COPY, possibly via a preprocessor like a Python script with psycopg2 if there's lots of mangled / invalid data.

If there are lots of tables, VBA (Visual Basic for Applications) or similar can be used on the Access side to automate the export, and your scripting language of choice can automate the import.

Alternately, you might be able to find an ETL tool that can connect to access and load into PostgreSQL directly. See if Pentaho Kettle, Talend Studio, CloverETL, etc can do it - possibly over ODBC if nothing else.