Can a VFR flight follow the same route of an approved IFR route (such as those found on Forefight Route Adviser) using waypoints and Victor airways?
Yes. In fact, before GPS came along, if you were flying somewhere and wanted to use your VOR to get from A to B, that's exactly what you did a lot of the time if it was convenient; fly along the victor airways if they were more or less on your route. IFR traffic is only separated from other IFR traffic and when VFR in non positive control airspace you can go wherever you want notwithstanding other restrictions.
In the GPS era nobody uses VORs very much any more and you can fly direct almost all the time when VFR (I haven't used the VOR in my plane in eons; mostly I just use a tablet or my phone), but there is nothing to stop you from flying along an airway if you feel like it.
For low altitude flights ie below FL180, yes you can. You can use either Victor (VOR) or Tango (RNAV) airways. You will fly at VFR altitudes during cruise, but use of these airways on VFR flights is common. For improved safety and traffic separation, pilots are requested to either file and open a VFR flight plan or request flight following when VFR on Victor or Tango airways, especially near navaids or other high density airspace.
Victor and Tango Airways can also be used for VFR flight segments during composite flight plans like VFR on top, VFR over the top, etc.
When filing a VFR flight plan with an ATS route identifier in it, consider the following: - check that the aircraft is equipped with suitable navigation aid receivers (e.g., ADF, VOR, GPS) - check the lowest altitude permitted for that specific ATS route - make sure the weather / clouds will allow you to climb and maintain the minimum ATS route altitude in VMC at all times - make sure to use VFR altitudes (xx500) , not IFR altitudes (xx000), as mentioned above already - specify the point, where you plan to join and leave the ATS route.
If something doesn't match, you can still fly the same direction and use the same navaids, but don't specify the ATS route in your flight plan. Instead, you can specify point along the ATS route with maximm 30 min flight time intervals.