Irtsgbr

Somebody took my things without asking me, without my knowledge and didn't return them back to me.

Is 'stolen' word appropriate to represent this situation? (e.g. He stole my things.) If not, what would be the proper word?

Stolen is the past participle of steal which is:

to take (the property of another or others) without permission or right, especially secretly or by force.
A pickpocket stole his watch.

So yes, stolen is an appropriate word to use when somebody took your things without asking you.

Welcome. Yes, "stole" or "stolen" means this.

• to take something without the permission or knowledge of the owner and keep it or use it:

... He never paid me back, so basically he ended up stealing a hundred dollars from me.

-- Cambridge Dictionary

The only exception I can think of would be if it was a person in authority, who was authorized by law to take it. This would not be considered stealing.

The police officer, under orders from a judge, took my things without asking me, without my knowledge and didn't return them back to me.

The tax authority took my things without asking me, without my knowledge and didn't return them back to me.

Technically, "stolen" is a suitable word.

However, depending on a number of factors, different people may use different words in different situations. Example: kleptomania is also stealing.

If confronted, the person might claim that it was a simple borrowing, but he did not have a chance to tell you or to return the object - yet.

Note: if that happened in an office (in other places also), using this word loudly, especially with several people present, will surely attract a bad energy on you, and it will destroy some of your reputation.

So in this case, it is much better (politically correct) to say: "took my things without asking me, without my knowledge and didn't return them back to me" - simply because "to steal" is a very strong word.