The material will be the easiest to make it look like in the images. Get that space nebula image, load it into a material, and use a ScreenPosition Node as input for the image UV. Setting the material to Unlit will offer a tick and cheap way to make it look like in the images you gave. Now you can do a lot more with it but this is a good base to experiment with it.
The particle effect will have to be a ribbon type.
Actually I looked now and someone seems to have made a tutorial for the exact type of particle effect you need.
You’ll have to modify it for your purpose though. Add a rough noizy texture for the alpha and that cool nebula material you just made.
EDIT: Scratch that, that is a poor tutorial. I did find this though.
https://answers.unrealengine.com/questions/54633/how-to-achieve-echoafterimageghosting-effect.html , Newest’s answer has you covered.