I recently moved into a 20 year old house. Don't know how old the gardens are. But the dalias and peonies and other long stemmed flowers need support to stand. Is there something I can do to amend the soil or some other thing to strengthen their stems? Thanks.

In a different forum last summer, I asked about my peonies and other long stemmed flowers, none of which can support their own weight. I was told the problem is not enough sun, which for my yard is likely true. No part of my yard gets full sun and some of those flowers got much less.
So for me, the bottom line was staking the flowers, which was easy and effective.

Maybe the cause of your problem is different, and can be fixed some other way. So this is just one possibility.

What gfs67 says is likely true. But without photos and a location, there's not much more we can do to help you.

Dahlia and Peony both have very sensitive rooting systems. Although some spring time fertilizer won't hurt any plant, don't dig anything in.

What jfs67 says certainly matches my experience growing dahlias here. The ones I planted in full sun needed no staking; but the ones in filtered sun tended to flop over.