What caused a measurable patch of Mt. St. Helens' ash to be deposited across Oklahoma?
I will propose an explanation. From experience I would say it have something to do with the US meteorological systems (systems as in masses of air) active the 18th of May 1980 and the week(s) after.

A bit of background : air masses can be high pressure (cool, and stable) or low pressure (warmer, more energy, more volatile, less stable). The next figure show in red a low unstable and warm system, and in blue a cool, stable system. (full website here)



Further, let's take into account the meteorological nature of Oklahoma - as an area in a volatile sector, where warm wet air masses from the gulf collide with colder, dryer masses from the west and the north - area part of what is broadly know as the tornado alley. On the wiki page for OK we see a typical system condition favorable for volatile weather. Green masses are warm, blue are cold and red is where the action is likely to occur.



Tornado or other frequent wild weather events are the result of a clash between those widely different air masses, temperature, moisture and pressures often leading to storm cells or other unpleasant windy/stormy situations.

Now let's get back to our volcano. I found those daily meteorological maps from the NOAA. When entering the proper dates, let's say 18th of May 1980 and the week after, we see the various systems in action. To keep things simple, I picked the 18th of May, and  the 21st. 



The 18th of May there was a low pressure system about right over the volcano - which was ideal to transport and displace a lot of ashes very far. The 20th, at 7:00 am, there was a Low in formation over Oklahoma which would become full fledged the 21st (see figure) and there was bad weather that day over Oklahoma City because of clashing cell. Eventually causing precipitation (rain and ash?).



I am not a climate-meteo-specialist, but I have good confidence that this scenario could explain a part of the reason why there is ash in Oklahoma.