Actually, most Vikings used spears in battle, because unlike what Hollywood, comics and fantasy try to tell us, the shieldwall was the battle formation of the day. They are also cheap and grant you good reach. A battle ax is also a very different beast from tools used for wood cutting and similar works. The blade tends to be much thinner and the entire head is often much more narrow. Getting as much force as possible into as small an area as possible. So while every viking might have had a tool ax or two, they were not used in battle unless it was a dire emergency. A proper battle ax is as specialized a weapon as a sword, though it was indeed cheaper to make (but than again still more expensive than a spear).
Small raiding parties not expecting much resistance might have used axes rather than spears, as they had no intention to fight in a shieldwall anyway. Though the evidence for that is mostly conjectural. The sagas would suggest so, but the sagas are that, sagas, stories that usually developed about some hero or another, not your average, everyday viking warrior.