Can I still continue to work if my EAD expires in about 3 weeks but I filed for renewal last month and am on J2 status?

Lawfully, you cannot work once your EAD expires.  YOU will have a gap in employment authorization and it can come back to haunt you later.  The safest thing to do would be to go off payroll once the EAD expires and then go back on payroll once you get your new EAD.  The EAD takes about 60-90 days to get so you should have filed for the extension giving yourself at least this much time if you wanted not to have a gap in employment authorization.