I supported my GF n her son in all of 2020 as she did not work. She will not file taxes for 2020. No taxable income. Am I eligible to claim them on my 2020 taxes?

You can claim a child, relative, friend, fiance (etc.) as a dependent on your 2020 taxes as long as they meet all of the following requirements : 

• You provided more than half of their financial support. More info 

• They made less than $4,300 in gross income during 2020 

• They live with you the entire year  

• They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident. 

• They aren't (or won't be) claimed as a dependent by someone else. 

• They aren’t filing a joint return with their spouse. 

• You are not being claimed as a dependent on someone else's return. 

So while you can claim them as dependents, including your girlfriend, assuming everyone lived with you all 12 months of 2020, you would not qualify for Earned Income Credit.  For someone to qualify you for this credit, there has to be a biological relationship or relationship through marriage.