How to calculate the total signal strength and phase shift of multiple signals in a reciever
This is simplified assuming there is not multipath occurring in the transmission (where the receiver would typically receive multiple copies of the same transmit signal at different delays resulting in multipath distortion which are typically addressed using channel estimation and equalization).

The OP's phase shift would all be relative since there is no common reference (clock) with the transmitter, so the comparison would be of the phase of the received signals to each other. A cross-correlation of the received signals in complex notation with the reference signal of what you know was transmitted would provide this.

This is accomplished by doing a multiply and accumulate of the received signal with the complex conjugate of the known ideal transmit signal, repeating the computation below for each possible offset $m$  (thus is the cross-correlation function specifically, correlating at each possible offset in time). 

$$XCorr[m] = \sum r[n-m]t^*[n]$$

Where (*) indicates a complex conjugate.

The magnitude of the correlation peak would be proportional to the signal strength, and the shift $m$ is proportional to the delay. With two signals at the same shift $m$ (in the same bin), the phase of the correlation is proportional to the carrier phase, giving a fine delay indication by comparing the phase result from two different receiver signals if they were in the same bin. In this case the signals would need to not be correlated themselves, otherwise the result would be the vector addition of the two (appearing as a single received signal). For this reason the transmit signals from each transmitter would be uncorrelated by separating them in frequency, time or code; and you can identify each one separately in receiver using correlation. 

Note the above computation for the cross correlation function can be done directly with FFTs given the FFT correlation property (which results in a circular cross-correlation):

$$XCorr[m] = \text{ifft}\{\text{fft}(r[n])\}\text{fft}^*\{(t[n])\}$$