What do the words じゃが and おるかの mean?

Question

Here are the sentences I have found these words.

1. 警察の者じゃが。
2. ジョーという少年はおるかの?

Answer 1

Those are good examples of what my favorite author [筒井康隆]{つついやすたか} has named 「[全国共通]{ぜんこくきょうつう}いなか[言葉]{ことば}」, which I would translate to "All-Japan Standard Provincial Dialect".

It is an imaginary dialect, instead of an existing dialect, that is used in stories. Believe it or not, it is most often used in children's stories. (Which is why I rarely recommend that beginning learners use children's stories as a study material. They will encounter strange sentence endings that they will not find in textbooks or even dictionaries.)

Practically all nationally-known children's stories take place in a small town on the country side, but they never tell you exactly where in Japan. The kind of Japanese spoken by the characters are virtually all in this imaginary dialect. Use a real, existing dialect and the kids, parents or teachers will not understand it unless they are from that area.

「[警察]{けいさつ}の[者]{もの}じゃが。」＝「警察の者ですが。」= "I am from the Police Department."

「ジョーという[少年]{しょうねん}はおるかの?」＝「ジョーという少年はいますかねぇ？」= "Is there a boy named Joe here?"

EDIT: An interesting (or rather funny) feature of this Standard country speech is that it is actively used in the Japanese translations of stories from outside of Japan as long as the characters are from the country side in their own country. Subbing and dubbing of foreign films are no exception, either. The city guys will be speaking Tokyo dialect and the country guys will be speaking this imaginary provincial dialect -- especially when the country guy is rather old.