Can a continuation be sold separately from the parent patent if no terminal disclaimers are in place?
Yes, absolutely, as long as there is not a terminal disclaimer that ties the applications together. A terminal disclaimer might be required during patent prosecution to avoid a rejection based on double-patenting. Under a terminal disclaimer common ownership of the covered patents is required. Both must be sold together with the requirement that they stay commonly owned.
Assuming no terminal disclaimer, there is no problem with selling or licensing the patents independently. An example of the strategic use of this might be the case of a core parent patent and several patents that issued from continuation or divisional applications where the other patents applied the core invention to different fields. Hypothetically a conceptually new type of saw blade (core patent) and child applications on a surgical tool, a tree trimmer and a potato peeler would make a good example. The patent owner could give non-exclusive licenses to four companies on the parent application and exclusive licenses each respectively for the surgical tool, tree trimmer and potato peeler. This example only fits the question if the parent had fully disclosed the three tools using the new blade or if the "sub-patents" were CIPs, a kind of continuation.
An alternative to an exclusive license is to actually sell a patent. This would be called an assignment. In my example the tree trimmer patent could be assigned rather than exclusively licensed.