There are a number of parts to this problem. The first is the strain gage. Generally, these are implemented via a Wheatstone Bridge circuit. Step 2 is conditioning the output of the Wheatstone Bridge, which can be pretty easily handled with an Instrumentation Amplifier. The final step would be the Amplitude Modulation with the 200KHz sine wave.
It's not clear to me what power supplies you've been given, which can have impact on your design. If you only have a positive DC supply you have to create a negative supply, or use integrated circuits that can handle single supply functionality and condition your signals a little bit differently.
It's also not clear whether you're given the 200kHz wave or need to create one. That might be what your 555 timer is intended to do, but its not necessarily how I would choose to create a sine wave. You might search on oscillator circuits.
Those are the level of pointers I'd give to a student. If you offer more info about the class, maybe its appropriate to offer more targeted help. As it is, the above search terms should be of some pretty major help.