In addition to what has already been mentioned (radioactive steam, ash, etc) some if it will probably end up getting burped up and forming part of the new land that always forms around volcanoes. Then in a few hundred years erosion will start wearing it away, carrying stuff that is still radioactive into the ground water and causing all kinds of problems.
Nothing reasonable. Even if you melt it, it remains radioactive and dangerous. At Chernobyl, for example, a big chunk of the core melted and essentially became lava, flowing down out of the core. It solidified as it cooled forming what they call the “elephant’s foot” structure., which is still highly radioactive. Completely melting it did not render it inert.
One does not simply carry nuclear waste into Mordor.