Way to home

You could also write "On the way home" or "The way home". It would sound more natural.

I was walking on my way home, and suddenly iI found peaa piece of paper on the ground, i. I picked it up and smoothed it out to be read...

"peace" means no violence, you need to use "piece" for "piece of paper".
Remember to add the "a" before an object you are speaking about.
I made this sentence into two sentences so it would sound more natural.

I noticed something soreally weird on it.

"So weird" is usually only used on its own, like when someone reacts "that is so weird!". You could also use "quite weird", "very strange", they all have the same meanings.