My dictionary considers them synonyms. Both mean to block or prevent something e.g a fallen tree obstructing traffic, an allergy impeding my breathing. I would more likely use 'obstruct' more often in everyday language, as it feels more common to me, but I often hear both. People (even native speakers) often say 'impede' when they mean 'impair', which has more of a sense of 'weakening' something, e.g 'I drank too much alcohol and this impaired my ability to think'

I disagree with the other answers. "Impedance" can be deliberate or positive. "The traffic designers impeded the flow of traffic on the feeder streets in order to achieve higher speeds on the highway" You could not substitute "obstructed" here. Corrosion in the pipes impeded the flow of water. (It slowed it down. Using "obstructed" here would suggest that it completely eliminated the flow.) "Obstruction" tends to be used for something that was irregular and negative. "The road was obstructed by the fallen trees." (could not substitute impeded, but you could say that "traffic was impeded" but it would be inferior) A common use of "obstruct" would be legal. "He obstructed justice" (could not use impeded) "My seats at the stadium had an obstructed view. That is why they were so cheap." (could not use impeded) My bowel was obstructed. My artery was obstructed. (Could not use impeded)

That's a good guideline.

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The words are synonyms, however I would use Obstruct for a physical issue (the tree is obstructing the road) whereas I would use Impede for something less tangible (My lack of fluency in Spanish is impeding my ability to communicate). However you can find plenty of examples where Impede is also used for a physical issue.