I'm trying to book a one way BNE-OSL in economy, but get V as the only option (apart from full Y). Is there any way I can book it in Q or higher in order to earn miles?

If booking on the Thai Airways website, first select origin, destination and dates, then you will go to the price/date matrix select as appropriate. Step 3 you will be asked to select flights and a fare type. A list should appear with Thai Saver, Thai Advantage, Thai Saver Plus, Thai Flexi Saver and Thai Flexi Plus. Each is specified with "no mileage accrual" or "mileage accrual". Select ones with Mileage Accrual and you will not be in V class.

Do you have dates?

The ability to select different fare types only works on roundtrip tickets. For one-way tickets, there's no way to choose anything but whatever it gives you, or to select unrestricted which gives you a Y fare. This is one of the big deficiencies of the TG booking engine. If you want some other booking class, you'll have to purchase it via TG by phone or in person, or via a travel agent or perhaps an online travel site that shows you the booking class (most do not).

If you're flexible with the dates/times, then you can sometimes find another date or time where V is sold out and so it will automatically give you Q. In the past where I wanted to book online due to a major hassle of booking at their office, I booked a date that didn't have V, so was able to book in Q, then called up TG and changed it to the date I wanted. But that Q fare didn't have any penalties for changing. If there's a penalty, then that method isn't so good. And often the ticket is not valid before the original date of travel, so if you use that method you may have to purchase it for an original date prior to when you want to fly, then call up TG to change it to a later date.

Not only does the ability to choose specific fare classes depend upon booking a r/t but it is also departure airport dependent.

Also, booking at an office will incur a surcharge, at least in Thailand that's the case.

try an agent

I'm trying to book a one way ticket, BKK-HKG in business on the TG website, and even when I click on the "Unrestricted" option, when reading the details of the fare rules/penalties, there is a 2000 thb penalty for any cancellation or change of the ticket.

I called the Thai ticket office in LA, and they said there was not a fare that was entirely refundable without a penalty.

So TG does not offer fully-refundable, penalty-free fares in business???

agree with Aussi_Flyer: do it the "old way" and involve your agent!
Only human people can be "reliable" and also made responsible, while for "online" bookings its always yourself who will be held "responsible".....

Right!

Even on domestic flights the only booking class that is available online is "J" and this involves canx fees.

i am booking on amex online tool where you can select any combination of booking classes