My family plays the game die Siedler von Catan a lot, wherein a large part of gameplay centres around people swapping goods. I’ve noted that we hardly ever use the word tauschen for the direct exchange to prevent just that ambiguity. If I have wood and I need grain (it’s not really straw in the game), we usually say:
Will jemand Getreide abgeben?
Will jemand Holz haben?
With these verbs it is always clear which direction you are talking about. We only use tauschen in a very generic way:
Will jemand mit mir tauschen?
Note that contrary to Barth’s answer, I initially understood the sentences in the wrong way, so it is definitely better to prevent any misunderstanding on the word choice level.