If a rogue planet disrupts Earth's orbit slightly to cause a long winter or summer will the Earth's orbit normalize back close its original orbit over time? Could a Planet X or some other elliptical orbit large body revolving around the sun effect Earth's orbit by being inside the inner solar system?
No. Basically, there is no such thing as a stable orbit in a realistic solar system. All planetary orbits are unstable due to gravitational interactions between planets, but how long it takes the instability to make a big change in a planet's orbit varies a lot. It can be a few of the planet's years, thousands, millions or billions. (Earth's orbit has been stable, so far, for 4+ billion years.) But stability going forward can't be guaranteed beyond at most a hundred million or so years.
The main source of instability is resonances. A resonance is where two planets are in orbits where the ratio of their periods is a simple fraction like 1/2 or 2/3 or 5/3 or whatever. Because of the simple relationship between periods, planets repeat the same configuration in space repeatedly, and gravitational interactions can build up. (Without the resonance, the interactions are just as strong, but in random directions and thus mostly cancel.)
Resonances can disrupt an orbit or can stabilize it. The Hilda group of asteroids are in a stable 3:2 resonance with Jupiter, for example, and Pluto is in a 2:3 resonance with Neptune. Both of these resonances act to stabilize the orbits. But the Kirkwood Gap in the asteroid belt is a 2:1 resonance with Jupiter which tends to keep the gap empty by disrupting the orbits of any asteroids that stray into the gap.
After the interaction, Earth will be in a new orbit and that orbit may also be stable over an extended period or it may be one where interactions with other planets quickly render the new orbit unstable. There's no way to tell without detailed orbital information on the encounter.
In any event, there is no restoring force to push Earth back to its old orbit.