strength on my hand

“I have no strength on my hand to lift this box.”
Is ‘on’ is the correct preposition for this sentence?

No. ‘In’.

Mister Micawber,
We used to say, “I went to school by car.”
Similarly can I say: “I went to school by foot.”

‘On foot’ is the usual phrase.

Mister Micawber,
“It is not in/at my hand to issue orders to dismiss him.”
Here is “in” or “at” suitable?

It is not in my hands = It is not under my control.