SSAS Deployment Wizard - Issue with multiple connection strings
What happened is that developers added new data sources instead of adding tables from an existing connection. In the future go to the Model menu... Existing Connections... Open. Then choose another table or query to import. This process is documented here. 

I don't believe there is a UI way of switching an existing table to use a different data source. The best approach is probably to just delete and recreate that table with the process above.

You should be able to delete the extra unused data sources from the Existing Connections dialog.