Pinning down Everwood's style on their third release, Without Saving, may prove a bit problematic or mystifying. Alternatively, this is a good thing as any band would like to be considered somewhat unique. Being on ProgRock Records lends to some obvious assumptions. But I'm not sure what have here is strictly progressive rock. Certainly, there's some versatile arrangements and fine musicianship. Perhaps sophisticated melodic hard rock is a good description.
There's much to explore on Without Saving not the least of which is the modern rock felt on Experience This and the lovely ballad Free. Certainly they are strong examples of Matyas Haraszi's strong vocals. Everwood can be accessible, offering the catchy hooks that make melodic rock both friendly and entertaining. Such is the case with My Own Vision and Insecure, both of which offer up tempo rock with little complexity. Conversely, you'll hear a bit deeper melancholy in Rain. Notes of progressive can be found here. Likely candidates would include the bit Eastern influence within Walls, the metalish Can't Find, but most certainly in the instrumental Pieces.
In the end, finding Everwood's Without Saving to be sophisticated, diverse, and eclectic melodic hard rock wouldn't be too far from the truth. Here's a solid album to get your head around, and that's likely challenging enough. Recommended.