I ja idem stepenicama kada nosim poklon.

Here I means also / too, not just and.

So I ja means I too or me too.

This usually appears when the speaker is adding themselves to something already mentioned:

• On ide stepenicama. I ja idem stepenicama.
  He takes the stairs. I do too.

So the sentence has a slightly contextual feel: it sounds like the speaker is saying they do the same as someone else.

Yes, idem already means I go / I am going, so ja is not grammatically necessary.

Serbian often leaves subject pronouns out because the verb ending already shows the subject:

• idem = I go
• ideš = you go
• ide = he/she/it goes

So why say ja here?

Because it adds emphasis or contrast.
I ja idem... = I also go... / I do too...

Without ja, the sentence would be more neutral:

• Idem stepenicama kada nosim poklon.

With ja, it sounds more like:

• I’m one of the people who does that too.

Stepenicama is the instrumental plural of stepenice (stairs).

After verbs like ići (to go), Serbian can use the instrumental to show the route or means by which you move:

• ići ulicom = to go along the street
• ići putem = to go by the road
• ići stepenicama = to go by the stairs / take the stairs

So stepenicama answers something like by what route? or using what?

By itself, idem stepenicama usually means I take the stairs or I go via the stairs.

It does not clearly specify direction.

If you want to be more specific, Serbian can say:

• idem uz stepenice = I’m going up the stairs
• idem niz stepenice = I’m going down the stairs

So in your sentence, the main idea is simply that the person uses the stairs rather than, for example, an elevator.

Here poklon is in the accusative singular, because it is the direct object of nosim (I carry).

• nominative: poklon
• accusative: poklon

These are the same here because poklon is a masculine inanimate noun. In Serbian, many masculine inanimate nouns have the same form in nominative and accusative singular.

Compare:

• vidim poklon = I see a gift
• nosim poklon = I carry a gift

But with masculine animate nouns, nominative and accusative are different:

• nominative: student
• accusative: studenta

It can mean both, depending on context.

Common meanings of nositi include:

• to carry
• to wear
• sometimes more broadly to bear / to have on

In this sentence, nosim poklon clearly means I am carrying a gift, because a gift is something you carry, not wear.

Examples:

• Nosim torbu. = I’m carrying a bag.
• Nosim kaput. = I’m wearing a coat.

Serbian present tense can cover both ideas, depending on context.

So:

• idem can mean I go or I am going
• nosim can mean I carry or I am carrying

In a sentence like Idem stepenicama kada nosim poklon, the most natural reading is usually habitual / general:

• I take the stairs when I’m carrying a gift.

It describes what the speaker generally does in that situation.

If you wanted a clearly one-time future meaning, Serbian would usually express that differently, for example:

• Kad budem nosio poklon, ići ću stepenicama.
  When I’m carrying a gift / when I carry a gift, I’ll take the stairs.

Both mean when.

• kada = full form
• kad = shorter, very common form

In most everyday situations, they are interchangeable:

• Kada nosim poklon...
• Kad nosim poklon...

The shorter kad often sounds a bit more conversational, while kada can sound a little more neutral or slightly more formal. But the difference is usually small.

Because Serbian has no articles like English a/an/the.

So poklon can mean:

• a gift
• the gift

Context tells you which meaning is intended.

In this sentence, English would usually translate it as a gift, because the meaning is general:

• when I carry a gift

If the context were specific, it could also be understood as the gift.

Yes, but it has a specific nuance.

I ja idem stepenicama kada nosim poklon. sounds natural if the speaker means I do too.

Because of I ja, it feels like a response or addition to something already said.

A more neutral version would be:

• Idem stepenicama kada nosim poklon.

You could also move the time clause:

• Kada nosim poklon, idem stepenicama.

All of these are grammatical, but they emphasize slightly different things.

Because ići stepenicama means to go by the stairs / take the stairs, which is the natural idea here.

Penjati se means to climb, especially to climb up. It focuses more on the upward movement itself.

Compare:

• Idem stepenicama. = I take the stairs.
• Penjem se uz stepenice. = I’m climbing up the stairs.

So idem stepenicama is the better choice if the idea is simply choosing the stairs as your route.

Yes. Both idem (from ići) and nosim (from nositi) are imperfective.

That matters because imperfective verbs are used for:

• ongoing actions
• repeated actions
• habitual actions
• general situations

That fits this sentence well, because it describes what someone generally does in a certain situation.

If you used perfective verbs, the meaning would shift toward a completed or single event, which would not fit this sentence as naturally.

So the imperfective forms help express:

• Whenever I’m carrying a gift, I take the stairs.