In OpenWRT, by default there is neither nohup nor screen , so the solution with only built-in commands should be to start the subshell using brackets and put it in the background with & :
(/root/wget/wget_download.sh >/dev/null 2>&1 )&
you can easily test this structure on your desktop, for example, using
(notify-send one && sleep 15 && notify-send two)&
... and then close the console before 15 seconds have ended, you will see that the commands in brackets continue to execute after closing the console.
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