This is totally hypothetical, but if these orbs and weird multicolored lights were actual physical craft I can in fact think of a physically plausible propulsion system that might look like that.
We know how to build two kinds of rockets: high thrust rockets with low specific impulse (Merlin, Raptor, SSME, F-1, etc.) and low thrust rockets with high specific impulse (ion thrusters). Excluding crazy stuff like thermonuclear pulse propulsion, we do not know how to build a rocket that is both high specific impulse and high thrust.
There is no physical reason to believe that such a thing is impossible though. We just don't (at least in the declassified world?) know how to build one.
A rocket that's both high thrust and high specific impulse would have a thrust whose particles are traveling at probably near relativistic speeds. Think of it as using a high efficiency high throughput particle accelerator as a rocket.
The performance of such a thing would be simply awesome, especially in terms of "delta-V budget" as per the rocket equation. In physics terms it's a plain old reaction engine but to someone ignorant of the tech it would look almost like anti-gravity or some other kind of magic.
Now here's where it gets kind of neat. What would such a thing look like visually if it were operating in the atmosphere?
Those crazy high energy exhaust particles would immediately collide with the atmosphere and emit light. The light would be a mix of the emission spectra of whatever the exhaust is made of and atmospheric gases. If the exhaust contained heavier stuff like metal ions the colors could be vivid and bright. Brightness and possibly color could change based on thrust and thrust vectoring.
It would look like a flying orb or a neon light show.
It would also be dangerous if you were anywhere close to it since it would kick off quite a lot of heat and probably X-rays or worse. If it were truly near-relativistic it would probably ignite small amounts of nuclear fusion in the atmosphere and emit neutrons and gamma rays too. I imagine that might give it a little more power too, like an afterburner from hell. I imagine there would be RF emissions as well.
The craft itself would be hot as hell too since the power requirements would be at least in the hundreds of megawatts. Even if the power source and thrusters had really high efficiency, the second law of thermodynamics would require the craft to dump at least tens of megawatts of heat overboard somehow. It would light up brightly in the infrared and be really obvious to FLIR.
Small craft using a thruster like that might look like flying orbs or multicolored light shows. A much larger more powerful one could probably attain velocities that would allow interstellar travel in "reasonable" time frames... for something with a really long life span or non-biological that is.
Again just speculation, but AFAIK does not violate any known physics and would match quite a lot of UFO reports.