Transaction log growing out of control on random times
If you are running in simple recovery mode, then the only transaction log data the full and differential backups will contain are for the very narrow time while the backup itself is in process, so looking at that is not going to help you here.

To see real-time activity, you can instead run the SQL Profiler.

Before I did that, though, I'd try a few other ways to identify open transactions:


Download and use sp_WhoIsActive, look at the open_tran_count and perhaps the start_time columns.
Run a query to show explicit and implicit open transactions.


Something like:

SELECT st.session_id, DB_NAME(sp.dbid) as dbname, at.name, 
    at.transaction_begin_time, sp.last_batch, sp.status, 
    RTRIM(sp.hostname) as hostname, RTRIM(sp.program_name) as program, 
    RTRIM(sp.cmd) as command, RTRIM(sp.loginame) as loginname
FROM sys.dm_tran_active_transactions at
INNER JOIN sys.dm_tran_session_transactions st ON at.transaction_id = st.transaction_id
INNER JOIN sys.sysprocesses sp ON st.session_id = sp.spid
ORDER BY transaction_begin_time


If you see something that has been running for a very long time, try doing a kill and see if the log clears up.