Mi koleras pro via mensogo.

Because Esperanto often uses a verb where English uses to be + adjective.

• koleri = to be angry
• kolera = angry (an adjective)

So Mi koleras is a very natural Esperanto sentence.

You can also say Mi estas kolera, and it is not wrong. The difference is mainly stylistic:

• Mi koleras = I am angry
• Mi estas kolera = I am angry / I am in an angry state

In normal conversation, Mi koleras sounds very straightforward and idiomatic.

Pro means because of, due to, or on account of.

In this sentence, it introduces the cause of the anger:

• Mi koleras pro via mensogo = I am angry because of your lie.

This is different from prepositions like:

• pri = about, concerning
• kontraŭ = against
• kun = with

So pro is the right choice when you want to show the reason something happens.

Because the phrase comes after the preposition pro.

In Esperanto, nouns and adjectives normally do not take -n after a preposition, unless there is some special reason such as direction.

So:

• pro via mensogo = because of your lie

There is no direct object here, so no accusative -n.

Compare:

• Mi aŭdas vian mensogon. = I hear your lie.
  Here vian mensogon is a direct object, so it takes -n.

Also remember that via agrees with mensogo, so if the noun does not have -n, the possessive adjective does not either.

Via is the possessive adjective built from vi.

• vi = you
• via = your

It behaves like an adjective, so it agrees with the noun it modifies:

• via mensogo = your lie
• viaj mensogoj = your lies
• vian mensogon = your lie (as a direct object)
• viajn mensogojn = your lies (as direct objects)

One important point: vi in Esperanto can be singular or plural, so via can mean:

• your (one person’s)
• your (more than one person’s)

Context tells you which one is meant.

Mensogo is a noun.

It comes from the root mensog-, which is related to lying or falsehood:

• mensogi = to lie
• mensogo = a lie / lying
• mensoga = lying, false
• mensogulo = liar

So in this sentence, via mensogo is literally your lie.

Depending on context, mensogo can refer to:

• one specific lie
• the act of lying
• a false statement

Here it most naturally means a specific lie or your act of lying.

Because possessives like via, mia, lia, ŝia, nia, and ilia normally make la unnecessary.

So Esperanto usually says:

• via mensogo = your lie

not:

• la via mensogo

This works much like English, where we say your lie, not the your lie.

Yes. Esperanto word order is fairly flexible.

The basic order here is:

• Mi koleras pro via mensogo.

But you could also say:

• Pro via mensogo mi koleras.

That puts more emphasis on the cause: because of your lie.

Even though the word order can change, the endings and prepositions still show the grammatical relationships, so the meaning stays clear.

Your sentence only states the cause of the anger:

• Mi koleras pro via mensogo.

It does not explicitly say who the anger is directed toward.

If you want to add that you are angry at someone, Esperanto often uses kontraŭ:

• Mi koleras kontraŭ vi pro via mensogo.

That means you are angry at/against you because of your lie.

So a useful distinction is:

• pro = the reason
• kontraŭ = the target of the anger

A simple pronunciation guide is:

Mi ko-LE-ras pro VI-a men-SO-go.

Esperanto stress is very regular: it almost always falls on the second-to-last syllable of each word.

So:

• Mi → one syllable
• koleras → ko-LE-ras
• pro → one syllable
• via → VI-a
• mensogo → men-SO-go

That regular stress pattern is one of the nice things about Esperanto.