When did the older English spelling of the endings of Isaiah and Elijah stop being used in the Catholic Church? I was reading Archbishop Fulton Sheen's Life of Christ and he always refers to Isaiah and Isaias and Elijah as Elias.  

I know that's one of the traditional English spellings, but when did it change for Catholics at Mass (at least in Latin translated Missals) and in other liturgical use?  

Not on topic here, but well appreciated would be an explanation of how one could come to pronounce -jah as -ias.
I think you'll find the question is not how -jah came to be -ias as how -ias came to be -jah.

For example you could look at the Greek rendering of the name Isaiah as see that it is Ἠσαΐας (pronounced Ēsaïās) which is a pretty clear indication that at one significant point in history the name was pronounced closer to the old/alternate English rendering of Isaias.

In general you will find names mutilated morphing from language to language and in a language over time as it gets to some persons ears and doesn't sound quite right. It's quite possible that at some point an Englishman's ear told him that ending a name with -ias sounded foreign and so he adapted it, however...

Pushing farther back however you will find the Hebrew name was יְשַׁעְיָהוּ (Yəšạʻyā́hû) so it might be that the more modern English rendition is actually an attempt to render an English name closer to the original rather than following the long tail of languages in between.

A similar story can be told for Elijah who's Hewbrew name would be אליהו (Eliyahu) but in much more modern usage is rendered إلياس, in Arabic (Pronounced Ilyās).

As for WHEN the change happened, it would see that for Isaiah, Isias might actually be a trendy thing started by a couple of writers in the mid 1900's. However the majority usage dating back to at least the 1600's KJV text is undoubtedly "Isaiah".