What type of sensors have complex Gaussian noise?
Do strain gauges also exhibit such noise?
No physical system suffers from, or produces, complex Gaussian noise. Quadrature systems can be modelled as being complex, with the in-phase branch corresponding to a real value, and the quadrature branch corresponding to an imaginary value. If each branch presents Gaussian (thermal) noise, then the noise can be modelled as complex Gaussian, too. However, this is just a modelling technique: the actual physical noise is never complex.
To answer your first question: sensors that operate in quadrature, and are modelled using the complex envelope, can be modelled as having complex noise.