The reason that a special oil is called for is usually to impart a subtle, extra flavor layer to whatever it is you're cooking.
I'd bet it is safe to say that 99% of the time you won't find a huge taste difference if you use another type of oil, as long as what you use as a substitute is mild flavored! (e.g. substituting sesame oil for walnut wouldn't be a such a great idea.)
Depending on what you're making, you could probably use canola oil without effecting the taste much. Or maybe some light colored, mild evoo or vegetable oil.
And if you really needed the taste of walnuts, you could always toast some (in a dry pan, over medium heat, until they start to smell wonderful, careful, they burn easily!) They could be ground up into to small bits after roasting too, if the size mattered.
If you ever do feel an urge to splurge there are some fantastic oils out there! Using a quality peanut oil in Asian cooking makes a world of difference. The taste of olive oils are about as varied as those of wines. I have a bottle of super stuff that I use to drizzle and for salads and a bottle of the grocery store variety that I use for everything else. Macadamia nut, sesame, lemon-infused olive oil mmmm all good stuff. But certainly not a requirement.
As someone who doesn't cook or eat meat, I've found that those kinds of things make huge taste differences in what I cook. Some folks splurge on filet mignon, me on champagne vinegar and oils!