How do you deal with your parents passing?

You take one day at a time. One box at a time.
If you have not talked to a Bereavement Counselor it might be time.
I can not relate to the loss of a parent as an adult. I was 11 when my Mom died and just over 4 years later my Dad died. And my Grandma died between the two of them. This was back when there were no "grief counselors, therapists, support groups" that kids would be able to talk about their feelings. My sister and I dealt with it day by day. To this day there are times when I get a bit melancholy and wonder what they would think of me as an adult. And I think about what it would be like to have been an adult caregiver for the 3 of them.
There is a little note above my computer that sorta helps sometimes.
Grief never ends
But it changes
It is a passage,
not a place to stay.
Grief is not a sign of weakness
nor a lack of faith.
It is the price of love.

I attack getting rid of things immediately so that I can move forward with my life. Avoidance really doesn't accomplish anything, and having their stuff around only makes is worse for you.

Seems that you are stuck, might be time for you get some grief counseling.

We are born to die, each day we are one step closer. While here, it is up to us to treat each day as a gift. The past is gone, the future unknown, today is to be embraced.

Going through their things really is a part of the process. If that's too difficult for you at this point, I recommend a grief counsellor or support group. When my Dad passed, I remember feeling really numb while going through all his things, but one things that helped was donating his clothing to a men's shelter. I did keep some shirts that I may sew up into a memory quilt or pillows at some point, but that's all. We donated his books, set aside stuff for all the grandkids, and chose some cherished items to keep for ourselves.