While authentic WWII German knives aren't junk, they were meant for ceremonial use, not actual cutting. The hardest thing they cut was a dashing look for the wearer in uniform. Sharpening them will abrade the chrome plating on the edge and open it up to rusting.
The possibility of it being a fake is fairly high, many were first copied and sold in the '50s by a British firm, sold to militaria and surplus stores. Most of that production is now 50 years old and carries much the same look and patina of age. The most typical of that lot is the parallelogram "Parachutist" folding dagger - which was never actually issued. The Knife Annuals have an article on them, the comments by actual Germans who lived in the era consider them interesting - but acknowledge they never had them.
Frankly, if the previous owner had a clue about it, it wouldn't have sold for so little. Just maybe it's authentic - even the Antiques Roadshow gets a winner - but the surplus, gun show, and knife community recognize most of the authentic ones travel in very close circles among serious collectors, with a great deal of provenance. There's simply more money in it to sell to a collector who's attempting to score the real stuff.