Khajit and Argonians, where did they evolve or originate from? Did Khajit evolve from cats? And did Argonians evolve from lizards?

Khajiit were apparently created by Azura, out of the Bosmer who lived in Elsweyr. However, the Father of the Niben says that there were inhabitants of the area that resembled the Khajiit even in the time of the Aldmer. Argonians are intelligent reptiles. Orcs were created by Boethiah when she ate Trinimac, and his followers (who were Aldmer) were transformed. But, the Father of the Niben makes mention of Orcs long before the Chimeri Exodus...

Orcs aren't a beast race though. They're a Mer race (Orsimer).

Khajiit and Bosmer are the Forest People.¹ Azura (Azurah) bound the Khajiit to the Lunar Lattice, so their form depends on the phases of the moons when they are born. (Y'ffre made the Bosmer to have one shape only, but some still know the shape-shifting magic required for the Wild Hunt.)

Argonians are descended from the Hist, the sentient trees of Black Marsh. Exactly how this descent worked itself out is unknown, but Argonians still demonstrate strong cultural or even biological ties to the Hist.

¹The Khajiit and the Bosmer are said to be too alike to leave each other alone. Q: Why do the Bosmer fortify the border with Elsweyr? A: If they don't, the border moves.

So the Argonians are actually the only natives off Tamriel?

There's the Hist, but most other native races are extinct, if they ever existed. They're referenced in Father of the Niben.

Correct me if I'm wrong but don't the Hist predate Nirn?

Nirn is the planet. No, they don't. Most of their realm was sunk beneath the sea in a war amongst the Ehlnofey.

That is a matter of some controversy. A particular reading of the Anuad suggests that the current inhabitants of Nirn came as refugees from an interplane(tary) war that literally resulted in entire chunks of planets (the "Twelve Planets of Creation") smashing into the surface of Nirn. The ancestry of Men and Mer can be traced to the Ehlnofey, a particular people from a particular place sometimes called "Old Ehlnofey". Some of them showed up on a chunk that landed on Nirn relatively intact: that was Tamriel, and their descendants are what we call the Elves. Others were scattered across Nirn, are known in the Anuad as the "Wandering Ehlnofey" and the ancestors of Men. The only other group that can be traced to this period (and I forget the precise details) were the Hist.

The Anuad then describes a war between the Wanderers, who expected a welcome when they finally found the lands of their brethren, and that era's inhabitants of what we now call Tamriel. There was collateral damage: much of the territory of the Hist was sunk; Black Marsh is all that remains (on this side of the ocean, anyway; there is a theory that the Tscaeci are related to the Hist of Atmora). Dreekius, an Argonian bartender, makes reference to a war that caused the loss of a lot of territory due to their lack of understanding of their neighbors (which Dreekius is a part of the attempt to remedy; his true job is a study of men). I think he may have been referring to the Ehlnofex Wars. My theory is that the Hist created the Argonians from certain tree-dwelling lizards as an "interface" with the descendants of the Ehlnofey.

I don't really think evolution applies here, they were probably created... it's much faster that way.