  "Strange" correlators provide a tool to detect topological phases arising in
many-body models by computing the matrix elements of suitably defined two-point
correlations between the states under investigation and trivial reference
states. Their effectiveness depends on the choice of the adopted operators. In
this paper we give a systematic procedure for this choice, discussing the
advantages of choosing operators using the bulk-boundary correspondence of the
systems under scrutiny. Via the scaling exponents, we directly relate the
algebraic decay of the strange correlators with the scaling dimensions of
gapless edge modes operators. We begin our analysis with lattice models hosting
symmetry-protected topological phases and we analyze the sums of the strange
correlators, pointing out that integrating their moduli substantially reduces
cancellations and finite-size effects. We also analyze instances of systems
hosting intrinsic topological order, as well as strange correlators between
states with different nontrivial topologies. Our results for both translational
and non-translational invariant cases, and in presence of on-site disorder and
long-range couplings, extend the validity of the strange correlators approach
for the diagnosis of topological phases of matter, and indicate a general
procedure for their optimal choice.
