vs living in a similar sized place inside Tokyo itself?

I did that for a while (like two months). The shinkansen pass for Odawara->Shinagawa/Tokyo costs about 70,000 per month (it's a bit more now due to the tax increase). May be reasonable if your workplace is close to Shin-Yokohama or Shinagawa or Tokyo, but if you're in a place like Roppongi, there is very little benefit. Plus the shinkansen that stop in Odawara don't run very often, and the last train is pretty early. (Don't know about the other shinkansen.)

Not particularly, since most employers reimburse your transportation costs (generally up to 50k yen, but I’ve seen 100k).