Οδηγήσαμε δυτικά.

Because Greek often leaves out subject pronouns when the verb already shows the person and number.

Οδηγήσαμε ends in -σαμε, which tells you it is first person plural: we.

So:

• Οδηγήσαμε δυτικά. = We drove west.
• Εμείς οδηγήσαμε δυτικά. also means We drove west, but εμείς adds emphasis, like we did.

Οδηγήσαμε is the aorist form of οδηγώ.

In this sentence, it is:

• 1st person plural
• active
• aorist

So it means we drove.

The basic verb is οδηγώ, meaning to drive (and sometimes to lead/guide, depending on context). Here it is clearly the everyday to drive.

This is the difference between two past tenses:

• Οδηγήσαμε = we drove
  
  • a completed action
  • simple past
• Οδηγούσαμε = we were driving / we used to drive
  
  • ongoing, repeated, or background action in the past

So:

• Οδηγήσαμε δυτικά. = We drove west.
• Οδηγούσαμε δυτικά όταν άρχισε η βροχή. = We were driving west when it started raining.

Here δυτικά is an adverb, meaning:

• west
• westward
• to the west

It tells you the direction of the driving.

So it modifies the verb:

• Οδηγήσαμε = we drove
• δυτικά = west / westward

No. Δυτικά can have different uses depending on context.

In this sentence, it is an adverb:

• Οδηγήσαμε δυτικά. = We drove west.

But in other contexts, δυτικά can also relate to western things or areas.

For example:

• τα δυτικά προάστια = the western suburbs
• στα δυτικά της πόλης = in the western part of the city / to the west of the city

So the function depends on the sentence. Here, because it is describing how/where we drove, it is best understood as an adverb.

Yes. Greek word order is more flexible than English word order.

The most neutral version is:

• Οδηγήσαμε δυτικά.

But you may also hear:

• Δυτικά οδηγήσαμε.

That version is more marked and may sound like the speaker is emphasizing west specifically, perhaps contrasting it with another direction.

So both are possible, but Οδηγήσαμε δυτικά is the most straightforward everyday order.

Yes. Both are possible, but they are slightly different in feel.

• δυτικά = west / westward
• προς τα δυτικά = toward the west

προς τα δυτικά is a bit more explicit and slightly fuller.
δυτικά is shorter and very natural.

So these are both fine:

• Οδηγήσαμε δυτικά.
• Οδηγήσαμε προς τα δυτικά.

No. It can be used without stating the vehicle.

Just like in English you can say:

• We drove for hours

Greek can also say:

• Οδηγήσαμε για ώρες.

If you want, you can name the vehicle:

• Οδηγήσαμε το αυτοκίνητο δυτικά. = We drove the car west.

But in many cases the object is unnecessary because the meaning is already clear.

A simple pronunciation guide is:

• Οδηγήσαμε ≈ o-thee-YEE-sa-me
• δυτικά ≈ thee-TEE-kah

More closely in Modern Greek:

• Οδηγήσαμε = /oðiˈʝisame/
• δυτικά = /ðiˈtika/

A few helpful points:

• δ sounds like the th in this
• γ before η sounds like a soft sound similar to y in this word
• the stress falls on:
  • γή in Οδηγήσαμε
  • κά in δυτικά

Yes. It is short, correct, and natural.

It sounds like a simple statement of direction:

• Οδηγήσαμε δυτικά.

A Greek speaker might also add more information, depending on context, for example:

• Οδηγήσαμε δυτικά για μία ώρα. = We drove west for an hour.
• Οδηγήσαμε δυτικά μέχρι την ακτή. = We drove west until we reached the coast.

But as a standalone sentence, it works perfectly well.