How to soften hard edges of images or objects in PhotoElements 2019 ?

Another way:

1. Select > All, or Ctrl+A

2. Select > Modify > Border. Enter the new size.

3. Optionally feather the selection a few pixels

4. Apply a Gaussian Blur

There are several ways to go about this. The simplest is to use the smudge or the sponge tool, and "paint" around the periphery of the object. It may do the trick for you depending on the object 

In the Effects panel, there are drop shadows and bevels that can be applied to a selected object.

It is also quite easy to apply a soft vignette. Try this:

• Open the picture file. This will bethe Background Layer.
• Open a blank layer above the Background Layer. This will be Layer 1.
• Activate the Elliptical Marquee tool, and on the tool's option bar set the feather value to 20 px. (If this turns out to be too much feather, you can start again with a lower value - experiment.) On Layer 1 engage the tool so that the oval embraces the object .
• Using the Paintbucket tool fill the oval with black
• Duplicate the Background layer and drag the Background Copy layer above the oval layer (Layer 1)
• With the Background Copy Layer still active at the top, group the 2 layers  - press CTRL+G.
• Turn off the visibility of the Background layer by clicking on its eye icon in the layers palette
• Open a blank layer above the Background Layer  - this will be Layer 2 - and fill it with any color to suit, or a gradient.