While reading on certain plants, I often read that some of their hybrid varieties are sterile.
While it seems clear that the plant will not produce offspring I'm not sure if it still produces pollen which is one of the main component of plant reproduction.
Does a sterile plant still produce pollen and nectar? Is it serviceable in any way for pollinators?
Sterility is not related to nectar production so a sterile plant may or may not produce nectar in the nectary. If the sterile plant produces pollen, then sterility is often due to chromosomal issues such as polyploidy.
It depends.
As Graham wrote, sometime it is just because of chromosomes: e.g. rejected by female flower, as not "correct".
But sometime just the flowers don't produce pollen, or just they don't have filaments (so they cannot carry anyway the pollen). See e.g. the roses. Wild roses have 5 petals. The hybrids have much more petals, but these were really filaments which became the additional petals. So hybrid roses doesn't carry pollen.
