When can I transplant these?

Hi everyone,
For the first time in my life, I have planted asparagus. This spring they went in to various locations and most have shown good growth. However.... our neighbour uphill keeps putting chemicals on his lawn (I don't know what it is, but I suspect an illegal weed & feed from years gone by.) It washes into our garden.
So I want to move the asparagus and strawberries.
Can I do that now, in the mid autumn?
Thanks!
Debbie
Barrie Ontario zone 5 continental cold temperate

I have read that fall is the best time to transplant asparagus, once dormancy begins, less of an impact on spring growth apparently. Strawberries can also be moved in the fall, though I've read that late august is when its usually done in colder climates.

Thanks Sean.

After the 1st hard frost - they need to be dormant.

Thanks, Marianne! Dormant they'll be.