You will need simply (but may be hard to apply) to measure the phosphorylation of downstream singling molecules using immunohistochemistry IHC or IF even better,
Int depends on type of target cell and tissue applied for,
then you will need a quantitative measurement of the fluorescence or colour density of the detecting antibodies, usually need a bit of optimisation experiments to select the optimal concentration and to create a scalable score , the use of multi-labelling using multiple markers limit your work as you may have to use cell specific marker too.
for example T cell marker CD3 and the phosphoprotein detecting antibody for example MAPK.
another higher complex method is to use CytoF system which recently has the advance to be applied on sections ...it will cost a lot !
Thanks for the additional comments! Unfortunately I don't think these approaches would be specific enough, because I'm talking about tissue sections and the mentioned downstream signaling molecules are not exclusively used by TLRs, so their activation doesn't prove TLR activation.