ODBC connection is similar to import. When you connect to OBIEE, Power BI imports the data into its in-memory cache. You can create visualizations from the imported data. To see the current data in OBIEE, you should refresh.
When you use DirectQuery, Power BI Desktop does not import or copy the OBIEE data. You can view the list of columns in Fact and Dimension tables. As you create visualizations by choosing the columns, data is queried from OBIEE via BI Connector. You always see the current data in OBIEE. DirectQuery works well with large multi-dimensional data sources such as OBIEE.
To learn more about the difference between ODBC and DirectQuery connections to OBIEE, please refer to our blog article on this topic.
BI Connector Server Edition is installed on the same machine in which the Power BI On-premise Gateway is installed.
Microsoft Power BI team is working hard to support DirectQuery for custom connectors on On-premise gateway. It is expected to become available in Q3 2018.