Sumif Formula or Sumproduct Formula? Three Criteria.

I'll try my best to keep this very simply and not over complicate.

I have a column containing dates, format dd/mm/yyyy. This is column B. Range B2:B1000.
I have a column containing data limited to only "NEW", "EXISTING" OR "LAPSED (+12 MONTHS)". This is column E. Range E2:E1000.
I have a column containing data limited to only "WON", "OPEN", "LOST" OR "DEAD". This is column J. Range J2:J1000.
I have a column containing monetary values. This is column H. Range H2:H1000.

Question: The return answer needs to the sum total of monetary value, identified as "LAPSED" AND "WON" AND within a specific month.

I need various other outcomes, such as "NEW" AND "WON" AND within a specific month but I'm sure I can figure those variables out on my own once I have a starting place from the above.

Many Thanks