Please, ask about emptying the Trash in the forum for your the system version of your Mac.
I never used Onyx, so I cannot tell, if it managed to put parts of the system software into the Trash.
The operation can't be completed because the item 'Library' is in use"; "The operation can't be completed because the item 'System' is in use".
The error messages you are seeing may be caused by the parts of the Time Machine backups in your Trash. But Onyx may have removed system components as well. If you are not sure, what you cleaned with Onyx, I would not touch the Trash without help from a system expert.
As to the Time Machine items in your Trash:
For the future: The only save and convenient way to delete items from a Time Machine backup is to enter Time Machine and ctrl-click the item you want to remove in the Time Machine star wars display. Then select the command "Delete all backed up items".
As the items are already in the Trash, you may try to use the Terminal to remove them as it had been described on Pondini's page: pondini.org/TM/E6.html - this website does no longer exist.
But here is a quote:
If the trash still won't empty:
Open a Finder window and be sure your Time Machine drive appears in the sidebar, or on your desktop. If it isn't, select Finder > Preferences from the menubar, then either Sidebar or General(for the desktop), and click the box for External disks.
Also open the Terminal app (in your Applications/Utilities folder). Be extremely careful when using Terminal. It is a direct interface into UNIX, the underpinnings of OSX. Unlike the Finder, there are few protections against making a mistake, which can cause untold damage.
In Terminal, the prompt looks like this: <Computer name>:~ <your name>$
(where <your name> is your short user name). It's followed by a non-blinking block cursor.
At the prompt, type the
and leave a space:
Now drag the Time Machine volume from the Finder Sidebar or desktop to the Terminal window:
When you release your
mouse, Terminal will fill in the "path" to the backups:
Note that if there are any spaces in the name, it will insert a backslash before them, as in the sample. That's correct.
The next p
the name of your Time Machine drive, as underlined in red here:
If it doesn't, STOP! Do NOT proceed.
If that's correct, copy this after the prompt: sudo rm -rf .Trashes
Then press Return.
You may see some warnings, and will be prompted for your Admin password (which won't be displayed). Press Return again. Nothing else will be displayed immediately.
If there were many items involved, this may take quite a long time. Unless there are problems, once the deletion is complete, you'll see another prompt (there's no progress bar or completion message).
Then Repair your backups, per item #A5.
For future reference, you usually shouldn't have to delete backups. But there is a way to delete individual backups, or all backups of selected items. See Time Machine FAQ #12.