Strong-field photoemission and electron recollision provide a viable route to extract electronic and nuclear dynamics from molecular targets with attosecond temporal resolution. However, since an ab initio treatment of even the simplest diatomic systems is beyond today's capabilities, approximate qualitative descriptions are warranted. In this paper, we develop such a theoretical approach to model the photoelectrons resulting from intense laser-molecule interaction. We present a general theory for symmetric diatomic molecules in the single active electron approximation that, amongst other capabilities, allows adjusting both the internuclear separation and molecular potential in a direct and simple way. More importantly, we derive an analytic approximate solution of the time-dependent Schrödinger equation (TDSE), based on a generalized strong-field approximation (SFA) version. Using that approach, we obtain expressions for electron emitted transition amplitudes from two different molecular centers, and accelerated then in the strong laser field. In addition, our approach directly underpins different underlying physical processes that correspond to (i) direct tunneling ionization; (ii) electron rescattering on the center of origin; and, finally, (iii) electron rescattering on a different center. One innovative aspect of our theory is the fact that the dipole matrix elements are free from nonphysical gauge and coordinate system-dependent terms: this is achieved by adapting the coordinate system, in which SFA is performed, to the center from which the corresponding part of the time-dependent wave function originates. Our analytic results agree very well with the numerical solution of the full three-dimensional TDSE for the H2+ molecule. Moreover, the theoretical model was applied to describe laser-induced electron diffraction measurements of O2+ molecules, obtained at ICFO, and reproduces the main features of the experiment very well. Our approach can be extended in a natural way to more complex molecules and multielectron systems.