The rotations of comets and asteroids are affected by outgassing volatilities. Io is very volcanically active. Does this give Io a varying orbit and a slow rotation? Tidal forces should take longer than the effect of a large eruption. Tidal locking means that any volcano alway pushes Io in the same direction (radially, tangential or inclined) accumulating the same kind of orbital change during all of its its active lifetime.
Is Io's orbit or rotation affected by its volcanism?
The rotations of comets and asteroids are affected by outgassing volatilities. Io is very volcanically active. Does this give Io a varying orbit and a slow rotation?
A similar answer to your question is provided at Quora's question: "Could the eruptions of all the volcanoes on Earth simultaneously knock it off its rotation or change its orbit?".
There are two differences: Eruptions on Io can reach escape velocity (2.558 km/s), and matter is subject to gravity as it is propelled away from the moon allowing some to escape and some to return; so it is a source of wobbling and rotational speed changes.
"Jupiter's rocky moon Io is the most volcanically active world in the solar system, with hundreds of volcanoes, some erupting lava fountains dozens of miles (or kilometers) high. Io’s remarkable activity is the result of a tug-of-war between Jupiter's powerful gravity and smaller but precisely timed pulls from two neighboring moons that orbit farther from Jupiter – Europa and Ganymede.
Orbit and Rotation
Although Io always points the same side toward Jupiter in its orbit around the giant planet, the large moons Europa and Ganymede perturb Io's orbit into an irregularly elliptical one. Thus, in its widely varying distances from Jupiter, Io is subjected to tremendous tidal forces.
These forces cause Io's surface to bulge up and down (or in and out) by as much as 330 feet (100 meters). Compare these tides on Io's solid surface to the tides on Earth's oceans. On Earth, in the place where tides are highest, the difference between low and high tides is only 60 feet (18 meters), and this is for water, not solid ground.
Io's orbit, keeping it at more or less a cozy 262,000 miles (422,000 kilometers) from Jupiter, cuts across the planet's powerful magnetic lines of force, thus turning Io into a electric generator. Io can develop 400,000 volts across itself and create an electric current of 3 million amperes. This current takes the path of least resistance along Jupiter's magnetic field lines to the planet's surface, creating lightning in Jupiter's upper atmosphere.
The tidal forces generate a tremendous amount of heat within Io, keeping much of its subsurface crust in liquid form seeking any available escape route to the surface to relieve the pressure. Thus, the surface of Io is constantly renewing itself, filling in any impact craters with molten lava lakes and spreading smooth new floodplains of liquid rock. ...".
The two-body problem explains how multiple interacting objects affect the orbit of each other. While the orbital eccentricity of Io is quite low (0.0041) the orbits of three of the Galilean moons (Ganymede, Europa and Io, excluding Callisto) have a 1:2:4 resonance. The "pushing" will act in periodic repetition to have a cumulative effect on the motion.
Orbital resonances greatly enhance the mutual gravitational influence of the bodies, i.e. their ability to alter or constrain each other's orbits. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be stable and self-correcting, so that the bodies remain in resonance.
The small effect of the volcanoes is corrected by the much greater effect of resonance. The website space.com estimates Io's age at about 4.5 billion years old, the same age as Jupiter. If the orbit was unstable and changing it may well have been destroyed long ago.