It surprises me that no one has mentioned this:
SR can easly at around 1:45 start to heal his wave while killing valk's creeps. Just make sure SR gets 2 judgements off so whole creepwave is dead (and your creepwave is full hp in case valk decides to counterpush using call) This results in a push and leaves valkyrie to an option - Skip a whole wave of exp and gold or take the rune. You'll also harass mid tower some.
I don't know if this works, but in theory it does (lol).
sr got more damage and the same range as valk
Please visit my thread if your tired of not having any pants http://forums.heroesofnewerth.com/showthread.php?t=401955
Thats hard setup, if you cant outplay valk. I think that valk isnt that good mid, but should still beat sr everytime.
SR wins easily if you focus on regen and stats items to out last hit Valk. Valk's base damage is pathetic.
Get roamers to camp the runes = GG Valk's rune control
Soul Reaper is a really bad hero to solo mid with, period. He can hardly gank, he is beat by almost every other mid possible, and his heal nuke is much better suited for a sidelane.
It's possible to win but SR is just a lot better vs melee heroes... In order to win you would need some early creep block, getting creep aggro and make sure to deny and last hit... As for rune control, you can control it if you have wards/someone from side lanes goes and checks it... This will give you the upper hand if done correctly... Also, make sure to keep the creeps on your side of the river and not stand in the open so valk wont arrow you.
If you are doing TMM and your buddy is a support hero, he could buy you a bottle while you buy some int items for higher damage... All heroes who are given that early bottle get the upper hand so this matchup of SR vs Valk can end up as a win/loss depending on how you initiate it