Sql-server – SQL Database size doesn’t match with the total table sizes in the database

When you delete from heaps, allocated space may not be unallocated unless you use a table lock. See "Deleting Rows from a Heap" from DELETE on MSDN

This is a separate problem to fragmentation (which happens of course)

Just in case, have you tried this to update usage info?

EXEC sp_spaceused 'MySchema.MyTable', 'true'

With no indexes or keys, you can't defragment it normally.
You can add/drop a clustered index, or do something like this

SELECT * INTO [MySchema].[MyTableNew] 
FROM [MySchema].[MyTable]
-- ORDER BY something

-- if you like
EXEC sp_spaceused 'MySchema.MyTableNew', 'true'

DROP TABLE [MySchema].[MyTable];

EXEC sp_rename 'MySchema.MyTableNew', 'MyTable';

oops: just seen updates, my Internets has been broken on and off...

Points, in no particular order:

• You do need the transaction log for a whole bunch of reasons I'm not going to go into. That said, if you're running out of transaction log space while you're in simple recovery mode, that probably means you have long-running transactions. Make your transactions as short as possible (gather all required user input before you start a transaction). (When SQL Server is trying to free log space, it can only free up to the start of the oldest current transaction.)
• Making NVARCHAR(MAX) columns nullable will not necessarily save you much space (off the top of my head it'll be 2 bytes per row, per column).
• Deleting/archiving old data will help you - with a caveat that it has to pass through the transaction log first.
• Shrinking your database will not help you, as a matter of fact it will kill performance (both while it's running and afterward, since DBCC SHRINKDATABASE uses a naive algorithm that almost perfectly fragments your indexes) and won't regain you much if any space.