The omni light shaders have a shadow intensity setting, but an alternative is to set up a light, without shadows, casting as much light as you want in the sahdows. Then make sure it’s selected, create a new light, click the More Options button and click the Copy selected light option. Set your new light to cast shadows, and set its intensity so that added to the intensity of the non-shadow light it gives the level you want in non-shadowed areas. Parent one light to the other and make sure you always use the parent light for adjusting position so that they stay in sync.
The darkness of a shadow is really the absence of light, and depends on the amount of ambient light coming from the rest of the environment, rather than from the light casting the shadow so as Richard says the way to lighten one is to add one or more lights that spill onto the shadowed area. Casting ambient light around a full 360 degrees and across the entire sky dome is one of the reasons I really like Light Dome Pro (and LDP2 when it was working).
As mentioned above, ambient light (i.e. general overall light level) plays a role in your shadow’s depth. Some 3D applications (Carrara) has a single setting for ambient light level that affects the whole scene at once. But DAZ Studio implements ambience on each individual surface in the scene. You could increase the general overall light levels in the scene by adding another light source (spotlight or distant light or even point light) to illuminate the whole scene or just certain areas in shadow. However this introduces numerous time consuming calculations in order to deal with multiple light sources. Fortunately, if you’re working in DAZ Studio and if the shadow is only obscuring a few objects or surfaces of those objects, then you can tweak up the “Ambience” setting for those particular surfaces. This adds to the brightness under the shadow without introducing the calculation overhead of an actual light source.
Additionally, cranking up the “Ambience” is also the way you can get a bright colored object to look as if it is glowing. Notice however, that the “glow” doesn’t cast new light onto nearby objects.
The next step in this direction is to have a glowing object that casts its own light on nearby objects. That technology is called “Radiance”. Unfortunately native DAZ Studio doesn’t implement radiance yet. Perhaps some 3rd party add-on light system can do that but I don’t have any of them to play with.