The German word meinetwegen is used in several different contexts. Its first meaning can be translated as "on my account" or "for me" in English.

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Ich weiß, ihr seid nicht meinetwegen gekommen.

I know you haven't come because of me.

Caption 3, Verstehen Sie Spaß? - Sascha Grammel

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Hat Themba wirklich nur meinetwegen ein Eigentor gemacht?

Did Themba really score a goal against his own team just because of me?

Caption 33, Die Pfefferkörner - Eigentor - Part 6

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It can also mean "for example" or "assuming that":

Und wenn du dich jetzt meinetwegen dort auf die Seite drehst...

And if you now turn onto your side, for example...

Caption 63, Die Schmerzspezialisten - Diese Schlafposition solltest du unbedingt vermeiden!

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Additionally, meinetwegen can also suggest indifference, translated as "for all I care" or even the very rude "whatever" below. 

Machen Sie doch meinetwegen, was Sie wollen!

But do what you want, for all I care!

Caption 61, Märchen - Sagenhaft - Der Rattenfänger von Hameln

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„Meinetwegen“, brummte Frederick.

"Whatever," grumbled Frederick.

Caption 42, Piggeldy und Frederick - Unendlichkeit

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Von mir aus is a colloquial expression, and can be translated as "for all I care," "as far as I'm concerned," or even simply "I don't mind."

In welcher Form auch immer... bis morgen früh von mir aus.

In whichever form… till early morning, as far as I'm concerned.

Caption 45, Fastnacht - Karneval - Quartier Latin

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Von mir aus bleibe ich ewig

I don't mind remaining forever

Caption 7, Max Giesinger - Nicht so schnell

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Was meinst du? -Von mir aus.

What do you think? -I don't mind.

-Vielleicht hat hier jemand was gesehen.

-Maybe someone here saw something.

Caption 43, Die Pfefferkörner - Eigentor - Part 2

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Further Learning
Take a look for additional examples on Yabla German and try working on your own sentences with meinetwegen and responses with von mir aus. 

Sounding like a native speaker in a newly acquired language can be tricky. There are all of those grammar rules and new vocabulary words and social conventions to be considered. One way you can make yourself sound more like a German speaker is by learning some of the common “filler” words people use in conversation. The word “well” is such a word in English. Let's learn some equivalent words a German speaker might use.

Here are two variations on ja (yes) which are used in this way:

Tja, was hat das mit Hollywood zu tun?

Well, what does this have to do with Hollywood?

Caption 6, Fastnacht - Karneval - Quartier Latin

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Na ja, das is' halt mein Titel, ja.

Well, that is just my title, yes.

Caption 83, Bürger Lars Dietrich - Schlecht Englisch kann ich gut

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Deciding whether to use tja or na ja is a bit of an art, but you can think of it this way: tja might also be translated as "hmm" or "let me think"; na ja might be translated as "you know."

Also, which is commonly used to mean “therefore” or “so,” often finds its way into conversations like this one:

Also, wir waren schon damals eigentlich...

Well, we were already back then actually...

Caption 33, Bürger Lars Dietrich - Schlecht Englisch kann ich gut

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When used as a filler, also is generally applied for one of two reasons. In the example above, it is used because the speaker is thinking back or reminiscing. It can also serve to add emphasis or impact to a declarative statement, like this one about a subject of controversy:

Also, da scheiden sich die Geister.

Well, here the spirits divide [opinions differ].

Caption 13, Fastnacht - Karneval - Quartier Latin

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Well, that's it for now! 

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Learning Tip

Trying to learn how to pronounce German? Go through a video that is short and sweet at least two or three times. Then practice saying the things that are said by the participants of the video. Take turns speaking each individual participant, so that you start to get the hang of some of the nuance of tone and pronunciation.