Мне нужно переодеться после работы.

Because Russian often expresses need with an impersonal construction:

• мне = to me / for me (dative case)
• нужно = necessary / needed

So Мне нужно переодеться literally feels like:

• To me, it is necessary to change clothes

This is a very common Russian pattern:

• Мне нужно идти. = I need to go.
• Тебе нужно отдохнуть. = You need to rest.

Using я here would be ungrammatical.

Нужно means it is necessary / need to / have to in this kind of sentence.

It is commonly used with an infinitive:

• нужно сделать = need to do
• нужно поехать = need to go
• нужно переодеться = need to change clothes

It does not work like a normal verb such as English need. Instead, it acts more like a predicative word in an impersonal sentence.

A useful way to understand it:

• Мне нужно переодеться = I need to change clothes
• literally: It is necessary for me to change clothes

Переодеться is perfective, while переодеваться is imperfective.

Here, the speaker means one completed action: after work, they need to change clothes. That is why переодеться is natural.

• переодеться = to get changed / to change clothes once, as a completed action
• переодеваться = to be changing clothes / to change clothes regularly, repeatedly, or as a process

Compare:

• Мне нужно переодеться после работы.
  = I need to change clothes after work.
  (one specific occasion)

• Я обычно переодеваюсь после работы.
  = I usually change clothes after work.
  (habit)

Not exactly. Переодеться usually means to change into different clothes or to get changed.

That is different from:

• одеться = to get dressed
• переодеться = to change clothes / change into something else

So after work, the idea is often:

• changing out of work clothes
• changing into home clothes
• changing into something more comfortable

In many situations, English get changed is the best match.

The ending -ся makes the verb reflexive.

Here that means the person is changing their own clothes, not someone else’s.

Compare:

• переодеть кого-то = to change someone else’s clothes / dress someone differently
• переодеться = to change one’s own clothes

So:

• Мне нужно переодеться = I need to change clothes myself

This reflexive ending is very common in Russian when the action is done to oneself.

Because после requires the genitive case.

The noun работа changes in the genitive singular:

• nominative: работа
• genitive: работы

So:

• после работы = after work

This is a fixed grammar rule:

• после урока = after the lesson
• после обеда = after lunch
• после фильма = after the film

Usually it means after work in the general sense, just like in English.

Russian has no articles, so работы here does not automatically mean the work. In this sentence, the natural interpretation is:

• after finishing work
• after getting home from work
• after the workday

So English after work is the best way to think of it.

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

The neutral version is:

• Мне нужно переодеться после работы.

But you could also say:

• После работы мне нужно переодеться.
• Переодеться мне нужно после работы.

These all mean roughly the same thing, but the emphasis changes:

• После работы мне нужно переодеться.
  emphasizes after work
• Переодеться мне нужно после работы.
  emphasizes changing clothes

So the original sentence is natural, but not the only possible order.

Yes. In many everyday situations, надо and нужно are very close in meaning.

• Мне нужно переодеться.
• Мне надо переодеться.

Both mean I need to change clothes.

A rough tendency:

• надо can sound a bit more conversational
• нужно can sound slightly more neutral or formal

But in most ordinary speech, both are perfectly normal.

Мне нужно переодеться and Я должен переодеться can both be translated as I need to change clothes, but they are not identical.

• Мне нужно переодеться = I need to change clothes
  sounds neutral and practical

• Я должен переодеться = I must / am supposed to change clothes
  sounds stronger, more like obligation, duty, or necessity

So if you simply mean I should change after work, мне нужно is often the more natural choice.

This is a very common Russian learner question.

• одеться = to get dressed
• переодеться = to change clothes / get changed
• надеть = to put on a specific item

Examples:

• Я быстро оделся. = I got dressed quickly.
• Мне нужно переодеться. = I need to change clothes.
• Я надел куртку. = I put on a jacket.

A classic rule:

• надеть something
• одеть someone

And:

• переодеться = change your own clothes
• переодеть ребёнка = change a child’s clothes

The main stresses are:

• мне
• нУжно
• переодЕться
• после рабОты

So the full sentence is pronounced:

Мне нУжно переодЕться пОсле рабОты.

The most important word to watch is переодеться, because learners often misplace the stress. The stress is on -де-:

• пе-ре-о-ДЕ-ться

And in работы, the stress is on бо:

• ра-БО-ты