RFM only works if i touch power supply line
You are missing the bypass capacitors on all of your ICs.

A quick check of the documents for the ATtiny84 didn't show a recommended value, but it does mention that bypass caps are needed.

Start with a 0.01µF cap as close as possible to the VCC and GND pins of the ATtiny. You will probably want to put one on the Op-Amp as well.  The RF module probably already has one, but it couldn't hurt to put one on it as well.

The biggest problem, though, is the one for the ATtiny.  Fix it first, then you will probably find that you are getting strange values from your straingage - bypassing the op-amp will then fix that.