Hotels in Oslo

Have you tried checking booking.com?

I’d also suggest checking the Thon hotels website.
https://www.thonhotels.com/our-hotels/norway/

The easiest way to get an answer is probably to contact the hotels.

There's a world of difference between Flam/Bergen and Oslo. Oslo is a business city that often has good deals on nice, business-class hotels in the summer. If a lot of the places near the train station are booked up, that suggests you may be bumping up against a special event of some sort. (I checked; it's not Taylor.)

I do my preliminary research on booking.com and sometimes make my reservations there--though this year I'm finding direct booking more consistently produces savings. If you are looking at chain hotels, you'll probably save an extra 5% or so by joining their affinity group.

I just looked at a random 2-night stay in late August and found the number of available hotels dropped sharply when I insisted on air conditioning. I guess a/c's not all that common in Oslo. I'd suggest looking at Oslo's actual, historical, day-by-day weather statistics for August over five or so recent years on the website timeanddate.com. Perhaps you'll determine you don't need air conditioning, which might open up a lot more possibilities. I don't know why Oslo's August data for 2021-2023 is missing, but here's August 2020.

Oslo weather -- August 2020

Use the pull-down box at the right, just above the graph, to change the month and year displayed.

You might try signing up for different hotels memberships which are free, but you get better prices and availability. Try Thon Hotels, we are going to Scandinavia in August/Sept., also - I joined Thon Hotel Membership - got better rates than I found on any other website. I made sure to book the category that was free cancellation and included breakfast.
Good luck!

Did you try Trip Advisor? they have multiple option for hotels etc.

We had a great stay at the Grand Hotel in Oslo. Large room, very good breakfast. Short walk from airport train. Good luck finding four rooms! We really enjoyed Oslo.

Highly recommend the Thon Hotel Cecil in Oslo. Excellent location and friendly, helpful staff. All the Thon hotels have great breakfasts and afternoon lounge amenities like tea and snacks. Would stay there again—as well as the Thon Rosenkrantz in Bergen. Excellent value.

I second The Grand in Oslo if you can get a room. Very comfortable, clean, quiet, and has air-conditioning. It is not common at all to find a/c in lodgings in Norway. It was an easy walk four our family from the hotel to the train station in the early morning when we were starting our Norway in a Nutshell part of our journey.

We stayed at the Thon Opera Hotel. Great location right outside of the train station. Great included breakfast buffet.