* Highly skilled/educated immigrants provide a significant boost to economic growth and pay more in taxes than they receive in benefits. I don't recall whether the podcast addressed the impact of these immigrants on the wages of highly skilled native-born workers.
* Low-skill immigrants are a net positive in the long term (i.e., once their children grow up) to the economy as a whole, but their net impacts in the short term are somewhat ambiguous, and there is some evidence that they bring about wage decreases for low-skill native-born workers. While that evidence is not completely clear-cut, it seems likely that there's at least some level of impact. There's also evidence suggesting that some of the displaced native-born workers "climb the ladder" into higher-skill, higher-wage positions when this happens, which may mitigate that impact.
From what I've read more generally, my impression is that outsourcing has a much larger impact on unskilled workers' wages than immigration does, though I don't have a specific source to support that claim.
[0] https://ftalphaville.ft.com/2017/09/15/2193785/podcast-the-e...
[1] https://ftalphaville.ft.com/2017/11/10/2195727/podcast-kim-r...