How does a student claim income from summer job where she invoiced the for hours worked/no deductions taken? No t4 or t4a, but wasn't running own business either?

You can report it as “Other Employment Income”. In TurboTax Online, click “Find” (magnifying glass 🔍) and search for “tips”. Then select “Tips, Gratuities, and Other Employment Income” from the list and click on the “Go” button. 

On the “Other Employment Income Sources” page, enter your amount in the top line, “Tips, gratuities or occasional earning not reported on a tax slip from the payer”, then click the “Continue” to save your changes.