  The direct experimental probing of locally varying lattice parameters and
anisotropic lattice deformations in atomic multilayers is extremely
challenging. Here, we develop a new combined numerical/graphical method for the
analysis of irregular moir\'e superstructures measured by scanning tunneling
microscopy (STM) on a small-twist-angle ($\sim$0.6$^{\circ}$) graphene on
highly oriented pyrolytic graphite (gr/HOPG). We observe distorted moir\'e
patterns with a spatially varying period in annealed gr/HOPG. The nanoscale
modulation of the moir\'e period observed by STM reflects a locally strained
(and sheared) graphene with anisotropic variation of the lattice parameters. We
use a specific algorithm based on a rigid lattice Fourier method, which is able
to reconstruct the irregular and distorted moir\'e patterns emerging from
strain-induced lattice deformations. Our model is universal and can be used to
study different moir\'e patterns occurring in two-dimensional van der Waals
heterostructures. Additionally, room temperature scanning tunneling
spectroscopy measurements show electronic states at the Dirac point, localized
on moir\'e hills, which increase significantly the apparent corrugation of the
moir\'e pattern. The measured topography is compared to classical molecular
dynamics simulations. Density functional theory (DFT) calculations confirm that
an AAB stacked trilayer region itself can contribute electronic states near the
Fermi-level, in agreement with the measured peak in the local density of
states. Furthermore, CMD calculations reveal direction-dependent bond
alternations ($\sim$0.5$\%$) around the stacking regions, induced by shear
strain, which could influence electronic properties.
