Our DM gave his permission to play homebrew archetypes as long as they are not OP. I'm thinking about paladin under the Oath of Death. RP wise it seems very interesting. However, according to a wiki it is possible to be unaligned, since there are existing figures that have chosen to be unaligned. Is this source valid? If not, what kind of alignment can I play to be close to this one?
That wiki article cites no sources and doesn't even say the game system that mechanic is intended for. It appears to be from 4th edition, where Unaligned was similar to 5e's Neutral.
In D&D 5e, unaligned is the alignment of a creature which does not have the sentience/intelligence to make moral choices. There for sure are no unaligned Deities. Only Beasts and other simple minded monsters are Unaligned. THis is in the PHB pp.122:
Most creatures that lack the capacity for rational thought do not have alignments-they are unaligned. Such a creature is incapable of making a moral or ethical choice and acts according to its bestial nature. Sharks are savage predators, for example, but they are not evil; they have no alignment.
If you don't want to be Good, Evil, Lawful or Chaotic then you can pick Neutral Alignment, which doesn't have any particular inclinations towards the mentioned philosophies.
From the PHB:
Neutral (N) is the alignment of those who prefer to steer clear of moral questions and don't take sides, doing what seems best at the time. Lizardfolk, most druids, and many humans are neutral.