Specific location where nerves converge
By reasoning, we can make the following distinction: 


the trigeminal nerve is a cranial nerve. 
the 2 others are peripheral
nerves.


Cranial nerves take their origin into their respective nuclei, and bypass the dorsal columns (main spinal tract for sensory information). Peripheral sensory nerves stem from the spinal roots, and from there go up through the dorsal columns. This would bring you to the thalamus, where all sensory information is regrouped. However, somatosensory information from the face and the rest of the body happen to travel through different thalamic nuclei (ventroposterolateral for the body, ventroposteromedian for the face, If my neuroanatomy is not too far behind me...). This leaves us with the internal capsula (fibers that link the thalamus to the cortex), but I do not think much signal integration occurs there. 

In conclusion, the first anatomical level of convergence between the 3 above-cited nerves would indeed be the somatosensory cortex.