SOA

http://www.infoq.com/resource/articles/applied-soa/en/resources/Applied-SOA.pdf

Legacy
Applications are built with internal logic to call each remote application/service they need to use. Kind of point to point integrations. With this approach, there are proprietery APIs, custom integration links and tight coupling of data and implementation

EAI
Connectivity between each application is based on middleware or message bus using EAI vendor's API which is proprietery