I have a couple of years of turbo tax on my local machine and a couple in the turbo tax cloud. can I move the local tax years to the cloud?

No they cannot be uploaded or merged.  

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year (it hasn't been updated with the new dates yet)

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-...

If you used the Desktop program before you may notice several differences and not like the online version.  It has less features and no Forms Mode.  You can only do 1 return.  Your return is only saved online so be sure to save both the .tax2020 data file and the pdf file to your computer when you are done.  In case you need to amend in the future or if you need a copy to get a loan or something.  You might not be able to access your online return when you need a copy.

No.  Returns prepared using desktop (CD/download) software are only stored on your own hard drive or any backup device you use like a flash drive.  They cannot be stored online in your TurboTax account.  The online account only stores returns prepared using the online program.