Depending on where you come from, you'll find there are not so many baby stores you'll randomly ran into in the city. You have to know where they are and where to buy what.
The biggest and most popular baby stores are Babyshop and Barnas hus. you'll find them both online and offline. They have everything (or almost everything) related to babies: clothes, strollers, beds, toys, etc. If you're interested you can subscribe yourself to their newsletter, they are on sales quite often and have many items on offer.
If you're looking for more "natural" baby products like cloth diapers, for instance, you might want to check out Bæreglede. They also sell pregnancy and breastfeeding clothes.
Another very cool online store is Jollyroom.no, where you'll find prams, furniture, toys and much more. They also have good offers every now and then.
Komplett.no is also very useful if you're buying bigger items, I find. I, for instance, bought our stroller and our babybjorn chair there. I guess we could say Komplett is like the Norwegian Amazon.
If you're looking for second hand stuff there is Finn.no, which you're probably already familiar with. This is the 'go to' place for any second hand thing here in Norway ;). For baby specific second hand items you should also check this Facebook group: IMOBAGO - Barneting / Buy, Sell Kids' items. You should be able to request access and get it granted in short time. It's basically a group where parents post items they're selling or items they're looking for.
If you find the websites just to be available in Norwegian, try right clicking on the mouse and hit "translate to English". Most sites should have this Google feature enabled.