There's a few parts to this question so there's more than one answer.
Earth gets knocked a little bit out of its orbit all the time by gravitational influence of other planets in our solar system. Jupiter and Venus are the primary two, but all the planets have some effect. These are called orbital perturbations and they tend to alternate, not add up. They're the causes of Earth's Milankovich cycles and the effect isn't negligible. These variations in Earth's orbit, which take thousands of years to move back and forth can cause the formation and recession of glaciation, sometimes called ice ages.
These orbital perturbations, in addition to being cyclical, as a rule, don't effect Earth's semi-major axis which is very consistent, and may only change slightly as the Sun loses mass.
Orbital perturbations can to lead to much greater variations of eccentricity and axial tilt. Mars, for example, undergoes much bigger variations than Earth, but it still undergoes a cyclical back and forth that leads to general stability within a range. All eight known planets in our solar system are thought to be relatively long term stable.
The exception to this cyclical back and forth is if there's a resonance where the effect can grow over time. The closest example of this in our current solar system is Jupiter and Mercury, where they're not in, but they're close to resonance and it's possible that Mercury will be tossed out of its orbit in a few billion years. It's the most unstable planet in our solar system.
This article isn't published, but I still think it's a good summary of both the stability of orbits in our solar system and the possible (but perhaps unlikely) destabilization of Mercury in a few billion years.
Planetary migration is another means for tossing a smaller planet out of its orbit. This is thought to be fairly common, based on observations of other solar systems and some uncertainty that gas giant planets could form close to their suns. (there may be room for debate on that), but migrating planets is thought to be fairly common, if somewhat slow. It's never been observed but it can be modeled. It's been suggested that when our solar system was young, Jupiter moved inwards, perhaps tossing Uranus and Neptune outwards and reducing the material available that would eventually become Mars and when migrating back outwards, leading to the late heavy bombardment which brought water to Earth. This is called the grand tack hypothesis.
An inwardly migrating Jupiter could certainly toss Earth about easily into a completely different orbit, but there's no evidence that suggests Jupiter is likely to migrate that much in the future.
A massive enough object from beyond the solar system could toss Earth into a different orbit and in doing so, not only change Earth's eccentricity and orbital plane, but change Earth's semi-major axis as well and that change would effectively be permanent.
A gravity assist of that kind could give Earth both a new eccentricity, a new orbital plane and a new semi major axis and perhaps a new set of Milankovich cycles, though I suspect over time, the orbit could re-circularize and the Milankovich cycles, largely reset to where they were, so there could be some correction not by the sun, but by the other planets orbiting the sun, but not everything would go back to where it was. The Semi-major axis change would likely be permanent and there would also be the question of whether the new orbit was in near resonance with other planets which would lead to further changes over time.
A higher eccentricity could create stronger seasonal variations and perhaps trigger a new ice age, or maybe fix man made global warming. :-)
The effects of a change in semi-major axis would change the length of a year, so, we'd need new calendars, and could warm or cool if it was big enough.
There would also be tidal concerns if a massive object passed close enough to significantly change Earth's orbit and perhaps even, pulling the Moon out of its stable orbit.
The good news is, space is big and quite empty and an object massive enough to change Earth's orbit passing close enough to do so is extremely unlikely.