依る
This word has implies going from one condition to another in a flowing, smooth manner. Hence, it has two main uses "to be due to, to be caused by" and "coming from X, it is so that Y."
Source of information.
When combined with と (I think the conditional/contrast marker). "coming from X, it is so that Y." Often used with some sort of Hearsay modifier like そう to denote that it's not entirely sure, because you heard it from there.
ホームページによると、それはとても簡単だそうだ According to the webpage, it is really easy.
天気予報に依ると、今日は雨だそうだ。 Based on the weather report, it appears that today will be rainy.
友達の話によると、彼女はやっとボーイフレンドを見つけたらしい。 According to my friend's story, she has finally found a boyfriend!
によれば, from 〜ば, has exactly the same meaning, but the difference in certainty between と and 〜ば still exists.
目撃者によれば、犯人は20代男性だ。 According to the eyewitness, the perpetrator is a male in his 20's.
ところに依ると
It is specific to useverb＋ , and requires coupling with something denoting Hearsay is a specific way to show a source of information: Not just where you have it from, but also how it was conveyed. Really awkward to transliterate.
先生に聞いたところによると、来週からオンライン授業になるらしいよ。 I heard from my teacher that it seems that we'll be doing online classes from next week onwards.
天気予報で見たところによると、明日は暑いらしい From what I saw on the weather report, it seems tomorrow will be hot.
ニュースで聞いたところによると、大きな台風が上陸するということだ I heard on the news that a a big typhoon is coming up.
先生が言うところによると、彼女は満点でN１に合格したそうだ Teacher said that she passed N1 with a full 100% score.
Depending on (different per)
also comes from 依る, but now more like "it flows out of the context".
人によって話が違う。 Depending on who you ask, the story will be different.
季節によって果物は美味しいくなったり、まずくなったりする。 Depending on the season, the fruit is either tasty or bad-tasting.
Ambivalent example:
それは、彼女によるね。 That is what she says, yeah That depends on her
に因る - because of
denotes that something is caused by something else.
it is a different flavour of よる, coming from {因|よ}る.
このミスは勘違いによるものです。 This mistake was because of a misunderstanding.
この地震による津波の心配はありません。 You don't have to worry about a tsunami caused by the earthquake.
由る - by (means of )
denotes that something implies the use of something else おじさんは盗賊による、命を{奪|うば}われた。 Uncle had his life taken away** by a burglar**
力によって決断する To settle it by using force.
カーテンによって{仕切|しき}ったところが僕の部屋だ。 The place that is divided up with the use of curtains is my room.
Made by me
When used with the Adversarial passive, describes that something has been created by someone. Not super common.
この歌は私によって書かれた This song was written by me.