The basic idea is that by high radiation exposure you have a small chance to gain a mutation, these have an equal chance of being positive as being negative, or possibly neutral.
There is a menu that shows current mutations and effects

Mutations have a few catagories:

.Stat changes
Self explanitory

Physical
These are usually equipped to replace certain body slots, or will replace textures of the player's skin.
They will have a deformed value, when this value goes too high (10) other people have a chance to attack you unprovoked.

List:

Positive:
.Scales, increases armour (deform 1)
.Chitinous armour, increases armour heavily, but also decreases agility substantially (deform 3)
.Spines, when something attacks you via melee, if it hits an area unprotected by clothing or armour, it will take a small amount of damage.
.Quills, an upgrade for spines (requires spines), triples the damage taken by enemies but comes with a deform value of 4, also torso slot (quills on back) removed
.Gills, water breathing
.Fur, protection from temperatures (deform 2)
.feathers, speed increase (deform 2)
.Night Vision, small night eye effect.
.High Night Vision, requires Night vision, bigger night eye effect (deform 1 at night and in low light levels due to eye glow.

Neutral:
.Webbed, webbed hands and feet heavily increase swimming speed at the cost of losing the gloves clothing/armour slot.
.Horns, additional melee damage (or like quills but with low enemy damage chance and a LOT more damage when it happens, head cripple chance halved and helmet slot removed (Deform 2)
.Claws, heavily increased unarmed, takes glove spot (1 deform)
.Thin skeletal structure, more easily crippled, lower carry capacity, + 5 agility
.Tail, provides an extra limb! can be used to trip enemies (deform 2)
.Possibility of becoming Goul, human NPCs like you less, goul NPCs like you more (deform 1 as gouls are still accepted into society)

Negative:
Night creature, stat decrease during the day, also if possible make bloom MUCH more powerful.
UV sensitive, You occasionally take a small amount of damage in sunlight.
Deformed, you are horribly deformed (Deform 4)
Badly Deformed, you are deformed a LOT worse (Deform 8, this mutation requires deformed)

Mutations can also be caused by mutagen, mutagen has a slightly increased chance of good and neutral mutation but is rare.

Mutations (apart from Goul) can be cured with Purifiers, these are even rarer than mutagen!

Obviously the modder would come up with more mutations and other ideas.

Here's my dream mod, I suggest someone makes it!

I'd actually had a similar idea before, as something that would work like an alternative to cybernetics.
You have a limited number of mutations that you can "slot" into your character by visiting certain doctors, and each mutation would have a mix of both positive and negative effects. Like a hardened skin mutation that increased base DT at the expense of Agility, or a feral aggression mutation that increases melee and unarmed skill at the expense of Charisma. Stuff like that.