Is a common dslr neck strap string enough?

Wearing my Nikon d7100 with a 24 to 70 lens as well as sb 700 speedlight makes for a hefty load. I even a common supplied strap strong enough, not to mention the little eyelets the strap goes into?

Yes it is, however it is never a good idea to let your camera hang from your neck.

That strap is to prevent your camera from accidentally being dropped in the middle of a shoot.

If you need both hands for something other than handling your camera, consider buying a device like one of the camera holster belts

My professional photographer son mounts his camera on a monopod to lighten his load.

The strongest strap is the one that comes with the camera.

The strap will hold, it's more your shoulder and neck that I'd be worried about. The strap your camera comes with is thin, which doesn't displace weight as well as aftermarket straps and harnesses.

I used to see fotogs hang one camera around their neck while they shot with the other. Now, more and more fotogs use a holster in front of their torso because it's safer for the camera AND lens. Those that use a strap risk bumping the camera and lens against something when they lean forward or stoop.

But to answer your question, yes, those straps are strong enough to support camera and lens but… The weight of some long lenses on the camera mount is what should be of concern; that's why fotogs using very long and heavy lenses hold onto the lens and let the lens support the camera that is lighter. Imagine the weight of having two cameras and two heavy long lenses hanging from the neck, imagine the aches and pains on the shoulders and upper back muscles after carrying that kind of load for a while.