calls to eradicate poverty are nonsensical, since poverty is defined in relative terms

The people who call for eradication of poverty are probably thinking in absolute terms.

But even if you define poverty in relative terms, it's still (mathematically) possible to eradicate it. In the UK, a typical measure of relative poverty is a household having less than 60% of median income (after housing costs). It would certainly be (mathematically) possible for every household to have more than 60% of median income, even if the income distribution remains highly skewed.