I sold all my stocks, but when I was trying to enter Various in date coulom, TurboTax did not allow me.

date acquired- various

date sold - enter the date.

I know the purchase date should be Various, but TurboTax does allow me to type letters (you can only put date). 

You are correct; however, there is a little trick. 

When you come down to enter the date there are two bullet circles.

• On one date is the default, but
• You can select Something other than a date
• The drop down menu will now allow Various