Basically, it depends on the material the nanogel is made of, and how it structures in the solvent. Nanogels are by definition soft matter material, and prone to change their size, shape and general structure depending on their environment.This makes any structure dependent measurement a bit of challenge, especially with imaging.
So, to answer your first question: Different nanogels look differently. Very few have actually been visualized in their 'native' state, and most of studies instead describe the nanogel by metrics which you can measure without actually seeing the sample, such as size, approximate shape, and outer/inner dimensions.
Scattering techniques such as the mentioned DLS/SLS, SAXS/SANS, and Nanosight will give you information about the size distribution either within your sample solution, or with the nanogel structures themselves, but won't really give you an image of your samples. The mentioned AFM technique will also give a size/shape/structure metric, but works by measuring the surface morphology of a stationary sample of your nanogel. Other techniques which may be suitable for giving these metrics are spin-spin coupling NMR, (FT)IR and Ramen spectroscopy, as these give information about which atoms/molecules are next to each other. And still, this will not give you an image of a nanogel. A drawing, perhaps, but not an image.
If your nanogels are at the limit of the nano definition (i.e. just above 1000 nm) , you might get a rough image of them with super resolution light microscopy, provided that the refractive index of the nanogels are a good deal different from the solvent they're in. Light microscopy has a hard resolution limit of 240 nm, so your image would be very blurry though. You could push the limit down to about 40 nm by using dyes, fluorescent probes and computational techniques. This however runs the gambit of altering your nanogel structure - especially if they are physically linked.
To go further down in resolution/scale , you could use electron microscopy such as SEM or TEM. These require a vacuum to operate and stationary samples to image, however. Note that SEM can only image surfaces, as it is based on the electrons scattered away from the sample, so you would need very low amounts of solvent, if any, for this technique to function. To image your nanogels in as close to a native state as possible, you would therefore have to either have to freeze them in their solvent and then image them by sending electrons through the sample (cryo-TEM), or solidify the sample in the solvent, and break open the embedding to image the nanogel (fracture SEM). All electron microscopy techniques are however also based on contrast - normally against carbon. This means that if your nanogel is made out of a 'simple' polymer having mainly oxygen and carbon, it will not show up on the images, as there is not enough contrast. It would be the same as trying to write white on white.
So, in summary: Few nanogels have been imaged, the best method to use will depend on the nanogel in question, a broad cookie-cutter method has yet to be invented.