First of all, Voyagers I and II have not reached the edge of the edge of the Universe, but they have reached the edge of our sun's Heliosphere (see image below, which shows the direction of our sun centered solar system as it moves through the interstellar medium, setting up a shock wave, left to right), the

final boundary of the area under the influence of the Sun; the two major components to determining its edge are the heliospheric magnetic field and the solar wind from the Sun.
Although Voyager I crossed the heliopause first, Voyager II offers new opportunities. It carries an operating plasma science detector, whereas its predecessor's stopped working years ago.
Once the heliosphere is well and truly behind Voyager 2, it will be able to tell scientists about the flood of interstellar wind pushing against the heliopause and about the local bubble surrounding the heliosphere. It will register lots of galactic cosmic rays, the incredibly high-energy atoms of a whole range of elements that are careening across the universe at nearly the speed of light.
"Galactic cosmic rays act as tiny messengers of our local galactic neighborhood," said Georgia Denolfo, an astrophysicist at NASA. "We're able to actually look at the galaxy through the clouded lens of our heliosphere and now take a step outside with Voyager and for the first time contemplate the vistas of our local galactic neighborhood."
Within about 300 years, the Voyagers will reach the inner edge of the Oort Cloud, the giant spherical shell surrounding the Sun, planets and Kuiper Belt Objects, made of icy, comet-like objects. The Oort Cloud's icy bodies can be as large as mountains. Crossing that field will take somewhere in the realm of 30,000 years at their current speed.
When the Voyager probes eventually leave our solar system, they'll settle into a long slow orbit around our Milky Way galaxy like our solar system does, for millions, if not billions of years; humanity's first messengers into the vast space which surrounds our barred galactic host (rendering below).

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