Once the spliceosome has cut out the introns from a pre-mRNA they are said to be degraded. What does that mean and is that happening in the cytosol? Can the nucleotides be used for something else within the cell?
Yes. Ribonucleases (RNAses) break down the spliced RNA strands back into mononucleotides, and these building blocks can be reused.
They will be broken down into nucleotide monophosphates, so they will have to be re-phosphorylated to triphosphates before they can be reused for transcription.
Here are a couple of reasonable reviews of the mechanisms:
Note: this one also mentions that sometimes introns are not fully degraded to single nucleotides, but instead can serve as signaling molecules.
Another use for a spliced out intronic piece of RNA is as noncoding RNA. Here's an example which include pre-mRNA also transcribing microRNAs.