How can I drop a Memory Optimized Table?
In addition to the restrictions pointed out in Evan's answer, there are a number of other things that can prevent dropping tables.  Most of them are similar to the restrictions on normal disk-based tables, and you should see them called out in your error message.  

For instance, if I have an in-memory table referenced by a natively-compiled (schemabound) stored procedure, I'll get this error if I drop the table:


  Cannot DROP TABLE 'YourTable' because it is being referenced by object 'sp_YourStoredProc'.


The solution in that case is to drop the stored proc first, and then drop the table.



The error message you're getting indicates that there is a server or database level DDL trigger.  You'll need to disable or drop those triggers in order to drop the in-memory table.  You can find any such triggers by running these queries:

USE [master];
GO
SELECT * FROM sys.server_triggers;

USE [YourDatabaseName];
GO
SELECT * FROM sys.triggers;


You should look into what these triggers are doing (auditing, perhaps?).  If it's safe to do so, consider disabling them with the DISABLE TRIGGER statement, then dropping your table, then using ENABLE TRIGGER to turn the triggers back on.

Note that server and database-scoped DDL triggers are different from object level DML triggers (which you mentioned that you checked for and there are none).