Yes, strength training should definitely be part of your routine NOW.
Without ST, up to 25% of your weight loss can come from lost muscle rather than fat. Muscle burns calories even at rest, and over time, this lost muscle can make longer term weight loss harder. And it is a lot easier to preserve your existing muscle mass through even a moderate ST program, than it is to add it back later.
ST is actually a very effective fat burner, and will help you achieve your goals.
Compound exercises are probably the best way to go, as they work several different muscles at once, allowing you to work most of the major muscles in your body in just a few moves. A simple routine might comprise:
* pushups (modified, incline or wall pushups if necessary)
* pull-ups/lat pull downs/bent over dumbbell rows