Organic Armour:

Padding, leather, bone or horn.

Sources:

Body armour of any kind is notably absent from contemporary Scandinavian depictions.
A document refers to reputedly effective armour of reindeer skin. As reindeer hide is thin and the hairs are particularly fragile, this is hard to interpret. If not an error, it suggests some sort of armour based upon reindeer skin, such as quilting.
There is no evidence that Vikings used thick hardened leather (such as Cuirboilli). There is a tantalizing rumour about an unpublished find in Denmark however.
Small plates of bone, horn or walrus ivory, used as scales or helmet panels have been found from other periods, but nothing conclusive from Viking Scandinavia.

All of these types of armour would have been relatively easy to make and generally cheaper than metal armour.

Quilting:

The use of some sort of padding under mail is not neccessary, but it increases the effectiveness of mail against shock and shallow penetrations, it is comfortable, and it protects inner clothing against dirt and chafing. Armour composed of quilting, felt or stuffing between two layers of flexible fabric or leather would have been relatively easy to make. It was certainly used just after the Viking period and may be depicted in the Bayeux Tapestry. Cotton stuffing probably first came into use with the Crusades as it could not be cultivated in northern Europe (the term Haqueton is derived from the Arabic for cotton).

There is a detailed description of making a Gambeson Here

An example of quilted armour The outside is leather. The padding is wool felt. The lining is unbleached linen (flax) canvas. Total weight is a little under 5 kg.

It is much easier to make this type of armour by first constructing flat pieces, then sewing them together.

Effectiveness:

Mostly from first hand experimentation: It is almost impossible to stab a sharp knife or even a spear through a couple of dozen layers of linen (or, for that matter hemp) canvas, although the wearer could still be wounded. It gets soggy in the rain. Wool or hair stuffing is less effective but sheds water better. Vikings only imported small quantities of silk, so they probably didn't use it for armour, although it is highly effective for its weight.

Thick leather:

Any thick leather offers protection, such as the Buff Coat of several centuries later. On the other hand the paucity of leather garment finds suggests that Vikings had something against it.