If Superman is nearly indestructible, so much so that everything from bullets to missiles ricochet off without a single scratch, wouldn't that mean that his body would feel completely ridged to anyone that wasn't him? I imagine that his skin would have the same consistency as stone. Just because he is indestructible, does that mean his skin would still have the elasticity of human skin? For instance if you were to touch the cartilage part of his nose, would it move or feel like steel? If this was the case, you would think that it would be an issue seeing as anybody who might so brush into him on the street as Clark might be suspicious as to why his skin was so rock solid. And poor Lois (or WW) having to kiss lips of steel!

Well, I know it's somewhat of a silly question, but if you have an answer please enlighten me.

Hard and tough are two different things.

I heard Superman's skin feels the same as human skin but cannot be injured.

It can't be pierced, shredded, burnt, or damaged by conventional means. The bonds between cells/molecules/atoms or whatever cannot be torn. That doesn't mean he's hard all the time (Giggity). I think of it like when something attempts to pass its energy kinetic, Kryptonian body rejects the exchange and results in the something taking damage. Poke him all you want, try to strike Superman and its like hitting a metal beam with a wooden bat, or just punching it.

Yes his skin feels like normal human skin if you touch him. He  has a solar powered an impenetrable aura which is activated by anything harmful- Bombs, Bullets, even dirt and bacteria.