There are several ways to do this, and it's hard to know which is best with no context about what you're actually doing with the data, but here are some options:
One way to do this is to make a content type representing each table (using CCK) with the foreign keys represented by type-specific node reference fields. Doing everything as nodes gives you a bunch of prebuilt functionality around nodes, but has a bit of overhead you may want to avoid.
Another option is to leave your database just like it is now. Drupal can do direct database queries, or you can use Data to expose your tables to Views.
Another option, if those referenced tables really only have 1 non-ID field, is to do the project_companies_assignments as nodes and do the other 3 as taxonomies. But this won't work if those are really more complex entities, and wouldn't be very flexible if they might become more complex.