The WoE Skulls have different applications for the respective Alignments. There are four kinds of WoE Skulls: Normal, Bronze, Silver and Gold.
If you haven't joined an Alignment, the skulls will not take effect, but you can still have them removed at the Friar.
Main article: The Chaos
Normal Skulls are the most common ones among the four, making Gold the rarest of them all. Therefore, the Gold Skulls will carry a higher weight or value when you sacrifice them to Hel.
Main article: The Order
The Order, on the other hand, because you are a defender of peace, getting blood on your hands is the last thing you'd want in the Kingdom. But sometimes, due to circumstances, you'll be 'forced' to spill blood. When you do, which is whenever you kill another player during WoE, it'll affect you physically, mentally and emotionally (so to say).
This feature is called "Burden". It can be linked very closely to the term used widely in movies about soldiers returning from tours/wars and most of them suffering from this "Post-Traumatic Stress Disorder" aka PTSD. Note that this only applies to followers of The Order and it doesn't apply to The Chaos.
So every type of skull you collect with have a certain effect on your efficiency in combat. You'll be affected physically, mentally and emotionally. However, you can distress yourself by talking to the Friar, who is found in Moonhaven (@jump 110 115).