House coat, bathrobe, robe, dressing gown.

Well, there used to be a powdering gown or powdering jacket, worn by a gentleman to protect his clothing while his hair or wig was being powdered. "This was ankle-length or slightly shorter, and wrapped over in front, often with long revers. Sleeves with or without cuffs." See drawing

Australian interpretation:

Bathrobe - terry-towelling type gown, used by male or female getting out of shower or bath. Robe would be an abbreviation for same.

Dressing gown - something you put on first thing in the morning getting out of bed, male or female. Thick or thin material, depending on the season.

Housecoat - obsolete, covering worn by housewives doing housework, not to be worn down the street.

Irish interpretation:
house coat as per Norah Batty - though also with sleeves,
Dressing gown- variety of materials worn after getting out of bed (or before getting in if you are a potterer) I have two a chinese silk for warm weather and a fleecy one for the other 360 days of the year.
Bathrobe big white towelling garment used as alternative to towel after bath or shower. Got one in a London radisson hotel as they had no towels left the day I arrived.
Robe would think of as formal eg degree conferring etc.
Slightly off topic Is there anywhere else apart from certain parts of Dublin city where children/teenagers wear their pyjamas walking down the street or in the local supermarket? .

As you know, I'm not a native speaker, but I'll answer intuitively as I do get quite clear pictures in my head!

Bathrobe:
Makes me think of a relatively unisex piece of clothing, either ankle length or knee lenght or something in between, with a rope-like belt. Could be terrycloth, silk or rough linen. Commonly worn after sauna or in the mornings before dressing.

Robe:
Could be same of bathrobe above, but could also mean something ceremonial worn e.g. at a university function.

Dressing gown:
Now this is the most feminine in my mind at first thougth. Something lighter than the bathrobe above, although a bathrobe made of silk could be a dressing gown.

House coat:
This one just makes me think of a piece of man's clothing. Kind of like a smoking jacket that's worn to casual parties outside your house/home, but this one a man wears at home. Whereas smoking jacket is most likely to be black only, a house coat is probably some other shade and the cut is looser, maybe longer too.

(I'm from Finland and Finnish is my mother tongue)

I like most of Kape's descriptions.

I would add to "robe" that it would apply as well, in its ceremonial form, to a judge's robes. Any photograph of the Justices of the U.S. Supreme Court, for example, would show them in that attire.

I would only argue with the description of "house coat." To me it would never mean a man's attire.

Slightly off topic Is there anywhere else apart from certain parts of Dublin city where children/teenagers wear their pyjamas walking down the street or in the local supermarket?

In Hong KOng old men will walk around in pyjamas.

Kape's house coat sounds more like a blazer.

A man's blazer to me is something different: the cut is different (both from smoking jacket and house coat) and you'd wear it outside your house. Basically the same cut as the top of man's suit, but a separate piece with a more variety (in colour).

In Hong KOng old men will walk around in pyjamas.

When I first arrived I presumed that there were just lots of people who had wandered out from an old people's home or a local psychiatric hospital!

What Kape calls a house coat I would call a smoking jacket. What Kape calls a smoking jacket I would call either a dinner jacket or a tuxedo jacket.

Arab men and boys sometimes wear pajamas on the street.

Mossadegh, the Iranian prime minister who was deposed by the CIA in the early fifties, was famous for appearing in public in pajamas.