Ovaj tjedan ne mogu uzeti godišnji, jer radim prekovremeno svaki dan.

Croatian often leaves out subject pronouns when they are already clear from the verb ending.

Here:

• mogu = I can
• radim = I work / I am working

So the sentence does not need ja. You could add ja for emphasis, but it is not necessary:

• Ja ovaj tjedan ne mogu uzeti godišnji...

That would sound more like I can’t take leave this week, maybe in contrast to someone else.

Ovaj tjedan means this week.

• ovaj = this
• tjedan = week

In this sentence, ovaj tjedan is a time expression. Croatian often uses the accusative for expressions of time span or the period currently being talked about.

So ovaj tjedan is a very natural way to say this week.

Yes. Both are common, and in many situations both can be translated as this week.

A rough difference is:

• ovaj tjedan = this week as a time period
• ovog tjedna = during this week

In everyday speech, the difference is often small, and both would be understood here.

Here godišnji is short for godišnji odmor, which means annual leave, vacation leave, or paid leave from work.

Croatian very often omits odmor because the meaning is obvious. So:

• uzeti godišnji odmor = to take annual leave
• uzeti godišnji = to take annual leave

This shorter form is extremely common.

Because the noun it describes is understood and omitted.

The full phrase is:

• godišnji odmor

Since odmor is easy to guess from context, Croatian often leaves it out and uses only the adjective:

• godišnji

This is similar to how English sometimes says something like the rich or the poor, where an adjective behaves like a noun-like expression.

It is in the accusative, because it is the direct object of uzeti.

• uzeti što? = take what?
• godišnji

In the full form:

• uzeti godišnji odmor

odmor is a masculine inanimate noun, and in the singular its nominative and accusative look the same. Because of that, godišnji also stays the same in form here.

This is a question of aspect.

• uzeti = perfective
• uzimati = imperfective

Croatian uses uzeti here because taking leave is seen as one complete action or decision: to take leave.

With modal verbs like mogu, Croatian still cares about aspect:

• ne mogu uzeti godišnji = I can’t take leave
• ne mogu uzimati godišnji would sound less natural here, because it suggests repeated or ongoing taking of leave, which is not the idea.

So uzeti is the normal choice.

In Croatian, most verbs are negated with the separate particle ne.

So you get:

• ne mogu = I cannot
• ne radim = I do not work / I am not working

Some negative forms are written as one word, such as:

• nemam
• nisam

But with mogu, the standard form is ne mogu.

It means I work overtime.

• radim = I work / I am working
• prekovremeno = overtime

Here prekovremeno functions like an adverb. The expression raditi prekovremeno is the normal way to say to work overtime.

Related forms are:

• prekovremeni rad = overtime work
• prekovremeni sati = overtime hours

Svaki dan means every day.

• svaki = every
• dan = day

This is a very common time expression. Croatian often uses this form directly for repeated time expressions.

You may also hear:

• svakog dana

That also means every day. In many contexts, the difference is very small, and both are natural.

Because jer introduces a subordinate clause meaning because.

So the sentence has:

• the main clause: Ovaj tjedan ne mogu uzeti godišnji
• the reason clause: jer radim prekovremeno svaki dan

In standard Croatian spelling, a comma is normally placed before jer.

Yes. Croatian word order is fairly flexible, and changing it often changes emphasis more than basic meaning.

The given sentence is very natural:

• Ovaj tjedan ne mogu uzeti godišnji, jer radim prekovremeno svaki dan.

But you could also say:

• Ne mogu ovaj tjedan uzeti godišnji, jer radim prekovremeno svaki dan.

That version puts a little more focus on ne mogu. Both are correct; the original sounds neutral and natural.