Although the mini-quasar at Murasaki 312 was creating a lot of ionization, the word "storm" wasn't used there.
Murasaki 312 from "The Galileo Seven"? The word "storm" was used in the episode
KIRK: I'm aware of that, Commissioner. At the same time I have certain scientific duties I must perform, and investigating the Murasaki effect is one.
...
KIRK: That thing out there has ionized this complete sector. None of our instruments work. At least four complete solar systems in the immediate vicinity. And out there somewhere, a twenty four foot shuttlecraft, off course, out of control. Finding a needle in a haystack would be child's play.
Captain's Log, stardate 2821.7. The electromagnetic phenomenon known as Murasaki Three Twelve whirls like some angry blight in space,a depressive reminder that seven shipmates still have not been heard from. Equally bad, the effect has rendered our normal searching systems useless. Without them, we are blind and almost helpless.
...
Captain's Log, stardate 2823.1. Our landing parties are on the surface of Taurus Two. We continue to hope.
Instruments are slowly returning to an operable condition as the ion storm slowly disperses. On the ship, we can only wait helplessly.
And some more specifics from TOS...
From "Mirror, Mirror":
KIRK: Report on magnetic storm, Mister Spock.
SPOCK: Standard ion type, Captain, but quite violent and unpredictable.
From "Court Martial":
KIRK: He may have blamed me that he never rose to command a ship, but I don't assign jobs on the basis of who blames me. It was Finney's turn, and I assigned him. He had just checked in with me from the pod when we hit the leading edge of the storm. Not too bad at first. I signalled a Yellow Alert. Then we began encountering pressure, variant stress, force seven, the works. I finally signaled a Red Alert. Finney knew he had a matter of seconds. I gave him those seconds and more. But apparently it wasn't enough.
...
UHURA: Meteorology reports ion storm upcoming, Captain.
...
HANSON: Approaching ion storm, sir.
KIRK: Warp factor one, Mister Hanson.
HANSON: Warp one, sir.
...
KIRK: Hold our course, Mister Hanson.
HANSON: Aye, aye, sir. Natural vibrations, force two, Captain. Force three.
...
CREWMAN: Engineering.
KIRK: One third more thrust.
...
That's the problem. How? Why? 'It just does' doesn't work for me. There has to be a reason.
That's kinda like how does warp drive work? Or phasers set to disintegrate? It's specific enough to convey the effects but smart enough to not get pinned down by the details. You could just use the "Galileo Seven" example and attribute it to an unusual quasar, the "Murasaki effect" as being able to ionize several light years in a very short time. Or make up something else that isn't already covered in Star Trek
As to traveling through an ion storm...
I'm not aware of any instance in TOS where you can't travel through an ion storm at warp or impulse. Now whether your ship gets heavily damaged or is destroyed is a different matter.
YMMV
