Imamo plan za vikend koji mi se mnogo sviđa.

In Serbian, subject pronouns are often omitted because the verb ending already shows who is doing the action.

• imamo = we have

So Imamo plan already means We have a plan.
You could say Mi imamo plan, but mi is usually added only for emphasis, contrast, or clarity.

Za here means for in the sense of for the weekend / for this weekend. After za, Serbian often uses the accusative case.

So:

• za vikend = for the weekend

The noun vikend is masculine, and in the accusative singular it looks the same as the nominative, so you do not see a form change here.

Koji means which or that in this sentence. It introduces a relative clause:

• plan ... koji mi se mnogo sviđa
• a plan ... which/that I like very much

It refers back to plan.

Because koji must match the noun it refers to, and also fit the role it plays inside the relative clause.

Here it refers to:

• plan = masculine singular

And inside the clause, koji is the grammatical subject of sviđa se:

• koji mi se sviđa = which pleases me / which I like

Since it is masculine singular nominative, the correct form is koji.

The verb sviđati se works differently from English to like. It is closer to to be pleasing to.

So:

• Plan mi se sviđa literally means The plan is pleasing to me
• natural English: I like the plan

That is why Serbian uses:

• mi = to me
• se = part of the verb sviđati se
• sviđa = is pleasing / appeals

Mi is the dative form of ja and means to me.

So:

• mi se sviđa = is pleasing to me
• natural English: I like

This is very common with verbs like sviđati se.

Se is a clitic particle that is part of the verb sviđati se. You should learn the verb together with se:

• sviđati se = to be pleasing / to appeal
• svideti se = perfective partner, often to come to like / to appeal once

In this sentence, se does not translate neatly by itself. It simply belongs to the verb.

Because the thing being liked is plan, which is singular, and with sviđati se, the verb agrees with the thing that is pleasing, not with the person who likes it.

So:

• plan mi se sviđa = I like the plan
• planovi mi se sviđaju = I like the plans

Since plan is singular, the verb is sviđa.

Here mnogo means a lot / very much.

• mnogo mi se sviđa = I like it a lot / very much

With sviđati se, this is a very natural way to intensify the meaning.

Yes, Serbian word order is flexible, but there are rules about short unstressed words called clitics. In this clause, mi and se are clitics, and they tend to come near the beginning of the clause.

So:

• koji mi se mnogo sviđa is natural and standard

Other orders may be possible in special contexts, but this one is the best neutral choice for learners.

Usually, no. In Serbian, the relative pronoun is normally expressed.

So English can say:

• the plan that I like
• the plan I like

But Serbian normally needs:

• plan koji mi se sviđa

Leaving out koji would sound ungrammatical here.

Serbian does not have articles like English a/an and the.

So plan can mean:

• a plan
• the plan

The exact meaning depends on context. In this sentence, English might translate it as either We have a plan for the weekend that I like a lot or We have the plan for the weekend that I like a lot, depending on the situation.

Not exactly, though they can be similar in some contexts.

• za vikend usually means for the weekend / this weekend / over the weekend
• vikendom usually means on weekends / during weekends in general

So in your sentence:

• Imamo plan za vikend = We have a plan for the weekend

That sounds like one specific upcoming weekend, not weekends in general.