Are railroad ties suitable for a retaining wall under tree canopy?
Where are you? Where I am from (Dallas TX)  railroad tie walls rot and shift. And due to the wood treatment chemicals in the ties there are environmental regulations which limit disposing of rotted ties.

I would not bring railroad ties onto my property, especially near a stream.

In Dallas "gabion walls" https://en.wikipedia.org/wiki/Gabion are used by the city to control erosion around streams. First rate private walls are of special concrete blocks (http://www.versa-lok.com/ or http://www.keystonewalls.com/).

I would do nothing to this property unless the house was getting undermined.

If you would make a tall retaining wall, you will have constructed a cliff from which people (especially children) and dogs could fall unless fenced at the top. It would be astoundingly expensive and unless constructed by someone with real expertise they can start to shift and lean.

EDIT
Building a 4' high retaining wall down near the stream would make a 4' drop-off at the stream. That would accomplish nothing positive, but would make a hazard there and interfere with stream flow under high water conditions.

EDIT #2
It is my understanding that the railroad ties commonly employed for "retaining" walls are used ties and are classified as "non-structural". These ties were removed from railroad beds and are re-sold for home landscaping. http://www.homedepot.com/p/Used-Railroad-Tie-Cresote-Treated-Common-7-in-x-9-in-x-8-ft-Actual-96-in-5100000070908000/100023488