You can make the Alt/Option level of Apple's US International PC behave like the version you are used to by creating a custom keyboard layout with the app Ukelele.

For reference the Alt/Option behavior of Windows US International is here.

Note that on a Mac both left and right alt/option keys normally do the same thing, i.e. create special characters.

PS If in fact your right alt key does not produce any characters at all, then something is broken with your keyboard or software.

An experimental keyboard that tries to conform to the Windows version can be found here.

Note: If you want something like one of the Linux versions of "US International" which have a dozen or more dead keys for making a huge number of diacritic and other characters, then the Apple equivalent is ABC Extended, whose layout is however quite different. For that see this earlier question.

You could try the US International keyboard layout, which supports most Western European languages. The non-ASCII characters are typed using a combination of AltGr (Right Alt) and letter keys. For example, you get an å character with the AltGr-w combination, and an ø with AltGr-l.

Most of the combinations are obvious; for instance AltGr-a results in an á character, AltGr-o gets you an ó. Unfortunately, since you can't have several mappings on the same keys, the combinations for å and ø are not the most logical. The layout is not the same as the one you have gotten used to on MacOS, which may also be a drawback.

I have used the US International layout for some years now, mostly because it is convenient for coding. I do write a lot of text in other languages than English, not just words here and there, and I got used to the odd combinations rather quickly.

For more information, see https://en.wikipedia.org/wiki/QWERTY#US-International

I have a US keyboard and a Danish keyboard set up with US keyboard layout. The Danish keyboard has the same number and shape of keys as the international English (which has one key more than the US), so my Danish keyboard works just like a US keyboard with the backslash and pipe character (/ and |) moved to a more "accessible" location.

And because I use these two for programming I prefer the international English keyboard layout (/ for escaping strings and regular expressions, and I use | when programming F#). So if you are using programming languages where these characters are used heavily, then I would recommend that layout.

You can always change the keyboard layout in the OS to make it work like a US keyboard if the other differences does not suit you. Of course you must be able to type without looking at the keyboard for this to work, because the characters printed on the keys will no longer correspond with what will actually be typed.

Or if you are really good at typing, you could just stick with the Hungarian keyboard, and change the keyboard layout. You can start by trying it out without having to buy one first.

I think the keyboard layout you are looking for is "ABC Extended" on Mac OS X El Capitan (10.11). If you are on an older version of Mac OS X this keyboard layout is called "US Extended", the rest of this answer uses the most recent name but everything else is the same between versions.

Here is how to enable either "ABC Extended" or "US International-PC".

In the Keyboard preference pane, click on the "plus" button in the lower left to add a new keyboard layout. Then select "English" in the next dialog box, scroll down to the bottom, select "ABC Extended" or whatever else you choose, and click "Add".

Here are the diacritical "dead keys" available in the standard US layout.

And here are the many more diacritical "dead keys" available in the ABC Extended layout, which provide for Eastern European and Slavic languages that use the Latin alphabet, along with other languages as well.

This screen shot shows the "option" keys in ABC Extended.

This screen shot shows the "shift-option" keys in ABC Extended.

Update

Here are other settings you need to be aware of.

Enable the pull-down menu on the menu bar. I would also un-check the box for "Automatically switch to a document's input source" because I find it too confusing in practice. But at least now you know where that setting is located.

It is also helpful to go to this pane and click the box to enable the Keyboard Viewer, so that you can see an on-screen floating window that shows you all the available diacritical dead keys in the layout that you have selected.

This is what the menu looks like (with whatever multiple layouts you wish to choose)

Here is where you can enable or disable the custom keyboard shortcuts to rotate among the list of different keyboard layouts which you have selected. I decided to disable these keyboard shortcuts because I found that it was too easy to accidentally rotate among multiple keyboard layouts and I was confusing myself as to which layout I was using at any given time. I would rather use the pull-down menu on the menu bar. It takes more time, but at least I am 100% sure of which keyboard layout I am using at any given moment.

You can choose whichever you prefer…

Adding US International PC as your input method will apply to either an ANSI or ISO keyboard, with almost the same results.

I would choose based on where you expect keys such as ` ~ § ± to be, as they move between the two physical layouts - ANSI has a 'missing' key left of Z compared to ISO, which will force your grave accent up to the very top left key, rather than next to Z.

So, the input source will adapt to whichever physical keyboard you use. This is British & US International on a UK English keyboard…

Both input methods also contain the standard Mac dead-keys on Opt ⌥

Go to system preferences/keyboard/input sources and use the plus and add buttons to activate the keyboard called US International PC. Then select that in the "flag" menu at the top right corner of the screen.

If you must have the Windows version of what the Option/Alt key does, try this custom layout.

US Standard.

For one, Apple only offer the option of US Standard in some territories now. US International exists for its close resemblance to UK version. Secondly, US Standard is the pervalant QWERTY across countries regardless of the manufacturer. Plus, symmetry. I guess if you need to re-learn where all the symbol keys are anyways, why not use the keyboard that doesn't have a symbol key left of "Z"? It's just better.

If you want you can install Karabiner, and remap "\" into "return" key, and map option+"\" back to "\". This way no worries about that annoyance.

Looks like you need to make the adjustment suggested in this Ask Ubuntu answer. Once you have done that, the English (Macintosh) keyboard layout probably fits your physical keyboard.

Edit:

If editing /etc/default/keyboard proved to not be persistent, the explanation might be that there is only one user on your system and that the change was silently wiped out when you added or removed input sources in Settings.

If you set it by running this command:

gsettings set org.gnome.desktop.input-sources xkb-options "['apple:badmap']"

instead it ought to stay.

(Looks like you hit a known inconsistency where GNOME and XKB don't play well together. That's a bug, and the issue is mentioned in passing in the discussion at bug #1892014.)