Those SDE_GEOMETRYnn tables are created when you create feature classes using GEOMETRY storage. Its a method to store CAD style data.
Where are you pasting this data from? Does it contain data, and if so does that data have CAD like data (true curves)?
As a temporary workaround, and test, can you create a new blank feature class in your SQL Server database, in the feature class creation import the spatial reference and fields from the source data. When the feature is created, can you then load the data using simple data loader?
Workflow:
Connect to SQL Server in ArcCatalog.
Create new feature class-> import spatial reference and fields from source data. Create the feature class using GEOMETRY spatial storage.
Right click the new feature class-> Load-> load data. Import the data from the source feature class.
