Έφαγα βιαστικά πριν φύγω για τη δουλειά.

Έφαγα is the aorist form of τρώω, and here it shows a single completed action: the speaker ate, and that action is finished.

A native English comparison:

• Έφαγα βιαστικά... = I ate quickly...
• Έτρωγα... = I was eating... / I used to eat...

So in this sentence, έφαγα fits because the speaker is talking about one completed event before leaving for work.

Βιαστικά is an adverb meaning hurriedly, in a rush, or quickly because you don’t have much time.

It comes from βιαστικός = hurried / hasty.

That is slightly different from γρήγορα, which just means quickly/fast in a more general way.
So:

• βιαστικά = quickly because of haste
• γρήγορα = quickly in general

In this sentence, βιαστικά fits well because the speaker had to leave for work.

Greek often drops subject pronouns when they are not needed, because the verb ending already tells you who the subject is.

So:

• Έφαγα already means I ate
• φύγω here already means I leave in the relevant form

You could add εγώ, but usually only for emphasis or contrast:

• Εγώ έφαγα βιαστικά, όχι αυτός.
  = I ate quickly, not him.

Without emphasis, leaving out εγώ is completely normal.

Φύγω is the aorist subjunctive form of φεύγω.

After πριν when it introduces a clause, Greek normally uses this kind of form. So:

• πριν φύγω = before I leave / before leaving

For an English speaker, this can feel strange because the main verb is past (Έφαγα), but Greek does not use a simple past form after πριν here.

So:

• πριν φύγω is correct
• πριν έφυγα would not be the normal structure in this sentence

The idea is: the eating happened before the leaving, and Greek expresses the leaving with a subjunctive form after πριν.

Because Greek and English organize time a bit differently here.

In Greek, φύγω after πριν is not a normal past tense form. It is the form Greek uses in this structure. The past meaning comes from the whole sentence and the sequence of events:

• first: I ate
• then: I left for work

So in English, depending on style, you might translate it as:

• before I left for work
• before leaving for work

Even though φύγω itself is not a simple past form, the overall meaning is still past because of the context.

Yes. Both πριν φύγω and πριν να φύγω are used in Modern Greek.

In this sentence, πριν φύγω is very natural and concise.
So:

• πριν φύγω = very common, natural
• πριν να φύγω = also possible

For a learner, it is safest to recognize both, but the version in your sentence is perfectly standard.

Here για τη δουλειά means for work or to work, depending on how naturally you want to phrase it in English.

A few important points:

• για can mean for, to, toward, depending on context
• δουλειά means work / job
• για takes the accusative, so τη δουλειά is in the accusative

Literally, it is something like for the work/job, but idiomatically Greek uses this kind of phrase the way English says for work or to work.

The article is normal in Greek. Greek often uses the article where English would not.

Compare:

• πάω στη δουλειά = I go to work
• φεύγω για τη δουλειά = I leave for work

The full form of the feminine accusative singular article is την, but the final -ν is often dropped before many consonants.

So both of these can occur:

• τη δουλειά
• την δουλειά

In this sentence, δουλειά starts with δ, and τη δουλειά is very common and natural.

So a simple learner rule is:

• τη = common shortened form
• την = fuller form, also correct

Yes. Greek word order is fairly flexible.

The original sentence:

• Έφαγα βιαστικά πριν φύγω για τη δουλειά.

is a very natural, neutral way to say it.

But you could also say:

• Πριν φύγω για τη δουλειά, έφαγα βιαστικά.
• Βιαστικά έφαγα πριν φύγω για τη δουλειά.

The basic meaning stays the same, but the focus changes:

• starting with Πριν φύγω... highlights the time frame
• starting with Βιαστικά... emphasizes the hurried manner

So the original order is not the only possible one, just a very normal one.