Večeras spremam torbu, jer sutra putujem vozom.

Because torbu is in the accusative case, which is the case used for a direct object.

The basic dictionary form is torba = bag.
But after the verb spremam here, the bag is the thing being prepared/packed, so Serbian uses the accusative:

• torba = nominative
• torbu = accusative

So:

• spremam torbu = I’m packing/preparing a bag / my bag

Because vozom is the instrumental singular of voz.

In Serbian, means of transport are often expressed with the instrumental case without a preposition:

• putujem vozom = I travel by train
• idem autobusom = I go by bus
• putujemo avionom = we travel by plane

So English uses by, but Serbian often uses the instrumental ending instead.

• voz = train
• vozom = by train

Because Serbian often uses the present tense for a planned or scheduled future action, especially when there is a time word like sutra.

So sutra putujem vozom literally looks like tomorrow I travel by train, but it naturally means tomorrow I’m traveling / I’m leaving by train.

This is similar to English sentences like:

• Tomorrow I’m leaving
• Next week I’m flying to Paris

You could also use a future form in Serbian, but the present tense often sounds very natural when the plan is already set.

The verb spremati / spremiti has a broad meaning: to prepare, to get ready, to put in order, and in context it can also mean to pack.

So spremam torbu most naturally means:

• I’m packing my bag
• I’m getting my bag ready

The exact English translation depends on context. Because the next clause says sutra putujem vozom, the idea is clearly packing a bag for the trip.

Because Serbian usually does not need subject pronouns when the verb already shows who is doing the action.

• spremam = I prepare / I am packing
• putujem = I travel / I am traveling

The endings already tell you the subject is I, so ja is often omitted.

You can include ja for emphasis or contrast:

• Ja spremam torbu, a on samo sedi.
  = I’m packing the bag, and he’s just sitting.

But in a neutral sentence, leaving out ja is the normal choice.

Jer means because. It introduces the reason:

• Večeras spremam torbu, jer sutra putujem vozom.
  = I’m packing my bag tonight, because tomorrow I’m traveling by train.

A common alternative is zato što, which also means because:

• Večeras spremam torbu zato što sutra putujem vozom.

Both are correct.
Jer is short, common, and very natural in everyday speech.

Because in standard Serbian punctuation, a comma is normally used before jer in a sentence like this.

So:

• Večeras spremam torbu, jer sutra putujem vozom.

That comma is the standard written form.

Not quite.

• večeras = this evening / tonight
• noćas = tonight during the night, often later at night

In this sentence, večeras fits because packing a bag is something you would normally do in the evening, before the next day’s trip.

So:

• Večeras spremam torbu = I’m packing my bag tonight / this evening

If you used noćas, it would sound more like you were doing it late at night.

Yes. Serbian word order is fairly flexible, because cases and verb forms carry a lot of grammatical information.

This sentence is natural as it stands:

• Večeras spremam torbu, jer sutra putujem vozom.

But other orders are possible, depending on emphasis:

• Sutra putujem vozom, pa večeras spremam torbu.
• Torbu spremam večeras, jer sutra putujem vozom.

The original version is a very normal, neutral way to say it.

Yes. Spremam comes from the imperfective verb spremati.

That matters because imperfective verbs are often used for:

• actions in progress
• repeated actions
• general ongoing processes

Here, spremam torbu sounds like I’m in the process of packing/getting the bag ready.

A perfective version would be spakovati or sometimes spremiti, depending on meaning. For example:

• Večeras ću spakovati torbu.
  = I’ll pack the bag tonight.

That sounds a bit more like focusing on the completed result.
The original spremam torbu is very natural if you simply mean I’m packing my bag tonight.

Yes, you could, but the nuance is a little different.

• sutra putujem vozom = very natural for a planned trip; often sounds more immediate or definite
• sutra ću putovati vozom = also correct, but slightly more explicitly future

In everyday Serbian, the present tense with a future time expression is extremely common for planned events, so sutra putujem vozom is often the more natural choice.