Jisho takes all the information from a separate dictionary database, and I'm not sure what their guidelines are for ordering meanings, but you'd think they would be roughly the same as any dictionary, where the most commonly used meanings appear higher.
For readings, presumably that's in 五十音順, the order of the Japanese syllabary. I don't see any reason to see why it wouldn't be.
According to http://www.edrdg.org/wiki/index.php/Editorial_policy :
"our goal is to reflect modern Japanese, so precedence should be given to sources that indicate up-to-date usage"
And I think what is also meant with that is that the senses should be in an order from "most likely to be the meaning" to "less likely to be the meaning" for a modern Japanese sentence.
Probably the meanings list are ordered from "most likely to be the meaning" to "less likely to be the meaning", but talking about the readings could it be the same (from most likely to be the reading)?
The reading ordination isn't completely random, because every time we type/search it will be the same, it's static. It can't be 五十音順, you can check out the illustration or a result like this: http://jisho.org/search/ue
How are meanings and readings ordered?
What's the order of the meanings of the entries and readings of kanji?
How does it work? Is it random or does it follow some rules?
Illustration: https://i.imgur.com/Sjc08FB.png