Do I need TurboTax Deluxe or Premier edition? I did not sell any stocks or mutual funds. I do have dividend earnings from my stocks, mutual funds and Roth IRA accounts.

If you only have Form 1099-DIV, Dividends and Distributions, then TurboTax Deluxe version is all you need.  

If you have any Form 1099-B, Proceeds from Broker Transactions, then you will need to upgrade to Premier.

Please see this TurboTax FAQ for more information about “Where do I enter 1099-DIV?”: https://ttlc.intuit.com/replies/5646867

I have investments in mutual funds, ETFs and stocks, but if I haven't sold anything for this tax year and maybe only bought some, is Delux still enough or would I still need Premier edition for some forms?

Deluxe will work if you had no sales. 

Even if I bought but didn't sell any, delux is enough?

Yes.  Then if you are using the Online version it will ask you to upgrade to Premier if you need to.  But if you are using the Desktop CD/Download program Deluxe it can do everything.  All the Desktop programs have the same forms. You just get more help and guidance in the higher versions. 

Unfortunately, Turbotax does not let me use Delux even if I have not sold stocks, bonds, mutual funds.

Did you get a 1099-DIV ?   Does it show Cap Gains in box 2a or anything in boxes 1a,  5 or 7 ?