So the first thing you need to do is establish the relationships between Vendor and Purchase Orders and Vendors and Vendor Contacts. You also need to establish a relationship between Purchase Orders and Vendor Contracts. This seems like it would be a one-to-one relationship, so the direct of the relationship should not matter.
Once these are established, create a form on the Purchase Order Table. Add the Related Fields "Related Vendor" and "Related Vendor Contacts" on this form. Them right click next to the "Related Vendor Contacts" field. Click on the option that says "Edit the Field Properties for this Field". Scroll down and check the Box that says "The Values in this field depend on a selection in another field":
Then select "A selection in [Purchase Orders : Related Vendor Contacts] shows choices where [Purchase Orders : Related Vendor] = [Vendor Contacts: Vendor]".
Return to the form and then the choices that you make in Vendor should populate the Vendor Contacts field with the related choices based on the relationship between Vendor and Vendor Contacts.