Yes, you can hold at an intersection with only the radial from one VOR identifying the intersection as long as you have either DME or GPS. And yes, you can hold at an intersection without DME or GPS if you have the intersection identified by the radials of two VORs. You can even hold with nothing but a GPS alone.
If you want to hold at a non-published hold position of your choosing, you could do so at a specific distance and direction from any identifiable point along a specific bearing from your hold fix. You can substitute the distance with the bearing from a second identifiable point. This includes NDBs, airports, Visual Reference Points, GPS waypoints, etc.
I always find it easiest to track inbound to the fix using either a radial, bearing, or GPS direct-to to the fix. When using VOR and DME, it is easiest to intercept the identifying radial way prior to reaching the appropriate distance. If you are using two VORs to identify the hold fix, intercept one of the identifying radials using one of your OBSs first. Use your other OBS to identify your second radial. Which OBS you choose depends on the radial or bearing of the fix along which you will be holding. That should be your primary OBS.
One of the holds given to me by the DPE on my instrument checkride was an unpublished hold at a self-declared, unofficial waypoint/fix. Since, I was on an IFR flight plan, I had to request the hold from ATC with the following format.
Skyhawkxxxxx, requesting a hold xx direction on a ### bearing, ## nautical miles and XX direction from intersection xxxxx, along the ### radial of xxxVOR, 1 minute legs, standard turn, at #### feet.
Admittedly, this was a bit of an over the top scenario given by the DPE. He was a legacy carrier captain who believed in making sure he tested beyond the capabilities of the magenta-line generation. It was more of a test of how I could think through, draw out , and communicate the hold while maintaining directional control under the hood rather than how to fly it. The bearing from the fix put me right in line with the IAF of my first IAP that had a hold-in-leau of procedure turn anyway.