Yes, mostly you can understand danish and norwegian if you can talk swedish (at least their written language). But there are some differences. They have some words that exists in swedish but means something completely else in their language.
If i dosen't remember it incorrect the Swedish and (i think it was danish) are closer related to eachother than the norwegian. But, i would say that the swedish people in general have it easier to understand the norwegians.
Between the Danish and the Norwegian language, me as swedish, can't see any difference in the written language between thos two countries.
I can give an example to you Seko.
Rolig:
In swedish it means funny.
In Norwegian it means calm(if my wife dosen't remember it wrong).
So reading the norwegian language and comparing it with the swedish might not give you a complete sentence. Or a sentence that make sense.
The same thing is with our "big brother" in our language group(the germans).
I have never studied german but understand lots of their written language. And also some of their spoken language.
Later on my father have remarried and i have got me a set of new grandparents, germans to be exact. And now i can even pronounce the german words correct.

But i can't still speak with a german person.
And there have been americans that have studied dutch that can understand a person that speaks swedish.
So if you can speak and write in one of the languages in the german language group, you may be able to somewhat understand the other languages in that group.
But Finnish are a language that really dosen't fit in. Their language cusins are down in the balkans. In the area of slovakia and downwards. If i'm not incorrect. You might know that better than me Seko.
The same relation might be there between the other language groups too.