The 'Victorian Era' is so long and encompasses so much, that it's nearly impossible to pick a trend or place or tune or much of anything. So I found a few sites on it, one really great one from the British Library. Or this one. This one is great (you need ActiveX to listen) Victorian Station.
Here are some children's songs, Nursery-songs.com. Again you can't listen to them only read the lyrics and see the illustrations. Worth it, but I'm not tune-ality inclined.
The Victorian Music Library allows you to borrow sheet music (at a cost). Here's their catalogue.
It was during this era that the gramophone came into use. Emile Berliner patented it, and records, in 1887. He was the first to use flat discs instead of cylinders. And was also the first to be able to mass produce them, making them cost effective and widely available. The first ones were made of glass, then zinc, and eventually plastic. [http://inventors.about.com/od/gstartinventions/a/gramophone.htm]
There are a lot of other musical inventions and I'm sure a lot of other websites out there with songs and recordings you can listen to. Anyone have a favorite?