Ask Mr. Smarty Plants

Using erosion-control blankets to stabilize the erosion area so that seeds have a better chance to germinate and become established would be a good solution. The erosion-control fabric works by slowing the runoff water and allowing sediment to fall out rather than be washed away. Seeds are sown under the erosion-control material and grow up through the matting when they germinate. Underneath the matting the roots of the plants growing through the erosion-control material anchor the soil to stop the erosion. If you use erosion-control blankets made of biodegradable material, they will eventually disappear leaving the plants to control the problem. Seeds can be sown under an erosion control blanket or grass plugs and other plants can be planted by cutting holes through the blanket.  This material is available at most nurseries.  In the linked article above from the University of Washington there are descriptions of other erosion control materials that can be used.  Your slope might also benefit from some of the other methods discussed there.

Grasses are effective for stabilizing slopes that are prone to erosion since grasses have extensive fibrous root systems that help hold the soil in place.  A monoculture of grasses alone is probably not the best solution but including some attractive native grasses is an excellent choice for controlling erosion because with their extensive fibrous root systems that hold the soil in place.  In combination with native woody and herbaceous perennial native plants, they would be very effective. 

Here are a few clumping native grasses native to Ohio.  Some of them grow higher than 3 feet but would not have a dense profile at their maximum height.

Sporobolus heterolepis (Prairie dropseed) grows to 2 feet and is perennial.

Elymus canadensis (Canada wild rye) grows 2 to 4 feet high and is perennial.

Koeleria macrantha (Prairie junegrass) grows 1 to 2 feet high and is perennial.

Andropogon glomeratus (Bushy bluestem) grows 2 to 5 feet high, is perennial and grows well in very moist soil.  It should do well in wet areas near the river.

Please note that most grasses grow best in full sun.  I don't know the light situation at your site, but there is one attractive clumping grass that grows well in the shade and also tolerates damp soil, Chasmanthium latifolium (Inland sea oats).  It grows 2 to 4 feet high, but its height can be controlled (see the species page linked above).

Here are some herbaceous plants and woody shrubs that would also be effective:

Mitchella repens (Partridgeberry) is evergreen and grows only to about 2 inches high in shade and part shade in moist areas and along streambanks.

Phlox subulata (Creeping phlox) is evergreen and grows in sun and part shade.   It does well on bare or freshly disturbed slopes.

Phlox divaricata (Wild blue phlox) also is evergreen but prefers shade and part shade and moister soil than P. subulata.

Amorpha fruticosa (Indigo bush) is a shrub that can grow as high as 6 to 10 feet.  It does very well along streamsides so might be a good choice for further down the slope near the river.

Ceanothus americanus (New jersey tea) grows to 3 feet and prefers shade or part shade.  It produces massive deep roots that help it withstand severe conditions and would also make it a good candidate for erosion control.

Dasiphora fruticosa ssp. floribunda (Shrubby cinquefoil) grows 3 to 4 feet and is noted for providing good erosion control.

Fothergilla gardenii (Dwarf witchalder) grows to 3 feet high and prefers part shade and plenty of moisture.

You can look for other possibilities in our Ohio Recommended list of commercially available native plants for landscapes in Ohio.