This is my first experience with SSIS so bear with me... I am using SSIS to migrate tables from Oracle to SSMS, there are some very large tables I am trying to transfer (50
Are you running your packages in parallel ? If yes, change to serie.
You can also try to divide this big table into subsets using an operation like modulo. See that example :
http://henkvandervalk.com/reading-as-fast-as-possible-from-a-table-with-ssis-part-ii
(in the example, he is running in parallel, but you can put this in serie)
Also, if you are running the SSIS package on a computer that is running an instance of SQL Server, when you run the package, set the Maximum server memory option for the SQL Server instance to a smaller value. That will increases available memory.