Any evidence of wealthy Scandinavians or Anglo-Saxons wearing padding under their helmets?

Helmets are pretty useless without some kind of padding/suspension.

Depends on if they are supposed to deflect blows or absorb them though. Even when we know for sure they had padding this is often much thinner than most people expect.
Whether for defence against blows or not, some sort of layer between the skull and the helmet probably was worn though, if only a woolen cap. Having a steel hat pushing directly at your head isn't the most pleasurable experience ;)

I wouldn't be surprised if padding was a wool hat and their bundled up hair. The viking era didn't possess many mass weapons and I think North men wore their hair long, so that acts like pseudo padding.

Apart from the Dane-axes being quite common, you also forget that Viking-age swords had thick blades and were really front-heavy, when chopped at full force they hit like a truck. Saxes could also reach almost a meter in length in some cases.

Viking Age swords were very light and maneuverable.

Blunt daneaxes are often more impact-heavy than sharp ones. Blunt viking swords are almost always significantly more clublike than sharp ones – they're normally made to match the profile and have thick edges, so consequently weigh a ton.

Regardless, an unpadded helmet is not 'almost useless'. It is almost useless against a blunt force strike, true (although it still has deflection and force distribution on its side). Typically modern fighters put a lot more concern into preventing impact injuries than seems to have been historically the case, and I suspect this is down to a combination of many modern blunts being quite unrepresentative clubs, along with a different set of priorities.

However, historical weapons are sharp. When someone slashes at your head with a sharp sword, a helmet without padding will stop them cleaving your head open, and so has been incredibly useful. This is a case where the different contexts of modern and historical fighting lead to very different requirements for useful equipment.

Most later helmet liners which do survive are much thinner than modern reproductions, and I suspect a similar thing applied to viking helmets (note also that we know they used little or no specific padding for mail). My inclination for a viking helmet would be a simple leather spider to hold the helmet in place at the right level, and a woolen cap if a little shock absorption is desired.

Obviously you might need to up-pad from that if you're doing modern combat games, depending on the requirements of your group and your personal safety principles, but it's important to understand that this is a modern adaptation.

Isleifur, you have two misconceptions here. One is that helmets doesn't work without padding, the other that swords are heavy or front heavy. Both are wrong.
My advice is to take the tips you've been given here and go with them.

Front heavy in terms of later doubled edged swords, but they were still swords. Swords in general are rarely front heavy enough to make good impact weapons. Type Xs are blade heavy when compare to later singled handed doubled edged sword types but they aren't maces are axes and they aren't near as club like as rebated steel versions people use for safety.

just my 2 cents but my helm is very thinly padded, single layer of thin sheepskin and thats it.... (its a single piece skullcap like helmet) and i have no issues with that....