Metro North will remain active and additional trains will be added in the event of a strike. However, trains will inevitably be PACKED and operating off-schedule due to all the extra time involved in taking on and letting off passengers. You might want to consider getting on in, say, Katonah.
(It will take 24 hours from the outset of any strike action for this additional service to be in place. (This amount of time is needed to reposition and reconfigure train equipment to provide special shuttle train service in the Bronx.)) See
mta.info for complete details.
The LIRR system will be somewhat more messy. Again, see mta.info.
NYC.gov Transit Information Center contains all City contingency plans: HOV, truck restrictions, temporary carpool rules, walking/biking info, ferry schedules, private bus skeds, temporary taxi law changes, an explanation of "dollar vans" and commuter train changes. Also lists Department of Education contingency plans (kids will love it!).