The wither on his W and his R were confirmed to exists in lore by his color story/Bloodline:
He slammed the butt of his long-hafted axe against the stonework, and a cloud of sand lifted from the roof. It hung there in shimmering veils, spinning in a slow circle around the hierophant and his warriors.
“What are you doing?” demanded the priest.
“I told you, I need to see your blood.”
In the blink of an eye, the circling sand became a roaring hurricane. The warriors raised their arms to shield their faces from the whipping sandstorm and the hierophant bent double, blinded and choking on windblown dust. The sandstorm howled with all the fury of deep desert winds that could strip a flock of Eka’Sul to the bone in minutes. Armor was no protection, the sand penetrating every nook and cranny to reach the skin below and scour it raw. The sun disc swung back and forth in the winds Nasus conjured, its supporting ropes pulling taut on the iron rings fitted to the stonework.
Nasus let the fury of the sands fill him, his limbs surging with power and his body swelling as the desert’s wrath manifested within his dark flesh. His form loomed and grew, towering and monstrous like the first Ascended were said to be.
Nasus tore Malouf’s sword from his hand, shattering fingers and tearing ligaments.
The demigod pounced on his attacker. Malouf’s body cracked under the jackal’s enormous weight.
...
A strange fragrance filled the air. Dead flowers spinning on lavender colored threads followed in his wake. Malouf twisted on the ground, the broken fingers of his right hand withered, skin sagging like wet parchment. The barrel of his chest caved in on itself like a rotting spine fruit.
The wither is probally associated with the disease that affected his body shortly before his Ascension, and made his entire body wither, when he Ascended he wasnt even able to walk, he was brought there by Renekton.
Meanwhile his ultimate seems to be an summoning of the power of the desert itself, this summoning may be something he learned over the centuries or an innate connection to the desert received with his ascension(but important to remember, it is A LOT easier for Ascended to learn/create new types of magic than it is to mortals).
Also about his E, in game it's called "Spiritual fire" iirc and he is able to summon fire in his lore, even though it is different from his in game skill:
Nasus roared and surged to his feet. A volcanic pillar of fire erupted beneath Xerath, and the magus bellowed as the shimmering fire of the Many Suns engulfed him.
And while this is still very different from his passive, he can regen his healt extremly fast in lore:
Nasus came to a halt in the midst of the rubble, his legs broken and twisted beneath him. His left arm hung uselessly at his side, shattered from shoulder to wrist. He tried to push himself upright with his good arm, but white hot pain surged up his spine where his back had broken. His body could heal these wounds in time, but he had no time left.
...
He shifted his weight, extending his legs and rotating his shoulders. His limbs were renewed, which meant he had spent a considerable time in darkness. His body healed fast, but he had no idea how long he had spent unconscious.