Free Electron Lasers (FEL) don't actually shoot electrons at things - they use electrons to produce light (coherent light, so it meets the requirements of being a laser). The electrons circulate around inside the device in a carefully designed way. The movement of the electrons is what produces the light. The useful feature of FELs is that they're somewhat tune-able. You can make a FEL spit out visible light if you build it right.
That's all a side topic though; all lasers, in space, regardless of their frequency, can't be seen... unless they're being shot into your eyes**. If your laser is in the visible spectrum, then you can see it reflecting off anything it hits. This is the light you see from a laser in darkened, smoky rooms. In space, there's no smoke, so you don't see a whole lot.
You would, reasonably, expect to see a beam of plasma. Plasma is hot. Very hot. And hot things glow. That is to say, they produce their own light.
Now, to neutrons. To the best of my knowledge, neutrons are not visible. They hold no charge, so they don't create light when accelerated, and neutrons don't contain heat like atoms do. Freely moving neutrons are unstable. They like splitting into proton + electron pairs. Each decay produces a photon up in the gamma-radiation range, so it's no visible either.
At the end of the day, there's a number of reasons why you don't want the beam to be visible. If you can see it at a distance, that means energy is leaving the beam to reach your eyes. That's energy that doesn't make it to the target. We generally call that waste, and inefficiency, and try to minimize it as much as possible.
** Ouch! I do not recommend looking directly at a laser beam.