You will file form 540NR Schedule CA for California, which performs adjustments for part year residents. The instructions will tell you to put the full moving deduction on line 26, Column A, and that if you moved OUT of CA (you did) to put $0 in Column E for use on your California return. You cannot deduct moving expenses on your CA state return for moving out of the state.
I'm not sure how to get that into TaxAct, even though I use TaxAct, and moved out of CA this year. I will be deducting our expenses on our 2017 return since we were reimbursed for most of our expenses by my wife's employer, but not until March 2017. If you are reimbursed in a subsequent year, you can choose which year to take the deduction.
I don't know anything about IL, we moved to NJ, where you can't deduct anything, including contributions to 403(b) or any other non-401k tax deferred account.