In what year did the motto's Novus Ordo Seclorum (New Order of the Age's), Annuit Coeptis (favors undertakings), and E Pluribus Unum (Out of many, one) start appearing on dollar bills?

Novus ordo seclorum and annuit coeptis since 1935.
E pluribus unum since 1796.
Wikipedia knows all.

Thank you Lefteh.
U da man

Glad to hear that from someone other than my mother.

hooray for lefteh!

How about why are these phrases on there in the first place?

They are on the Great Seal of the United States. They help summarize the feelings and intentions of the Founders.

Well I was tryin to pry a bit deeper into that point. I think its a bit curious that the references to the ‘new order of the ages’ (new world order?) and favors undertaking were added relatively recently (140 years after the part about standing together as one). I will agree they are intended to summarize the intentions of certain individuals. Although I don’t think it is a tribute to George Washington

They were added to the currency somewhat recently, but they’ve been on the seal since the 18th century.

I get that, but that begs the question of why did they not get added until recently considering they have been around so long?

First of all, novus ordo seclorum doesn’t mean New World Order. That’s simply a bad translation, or a conspiracy-theorist-y spin on the true translation of new order of/for the ages. It was borrowed from Vergil during the Revolution to describe the feelings at the time. There would be a new order, new authority in this land and it would last the test of time.
Secondly, Roosevelt made some major changes to the dollar bill. He decided that in that trying time, when there was mass confusion in regards to gold and American currency, the addition of the Seal of the United States would be an appropriate addition to its money.