Is there a hard and fast rule on how to slur notes for Celtic and Irish jigs and reels? I have listened to many people play this kind of folk music (Alasdair Fraser, Deborah Klemme, Eileen Ivers...), and I can't seem to get my music to have the same rhythm as theirs (i.e. it doesn't sound folk; it sounds like me trying to play folk).
There is not a hard and fast rule, but there are lots of loose guidelines.
Here are a few places to get started.
1) Emphasize the off beats. In dance music, the phrases will usually start on beat 1, but a strong off beat will pull the dancers along.
2) Slur across the beats. A beginner will often slur the notes in a jig as 123 456. An experienced player won't. In 4/4 time, 1&2 &3& 4 & is called a serpentine bowing pattern, and shows up often.
3) Learn a couple of ornaments, and pay attention to where your favorite artists use them.
Keep on listening, and if you can, find people in your area to listen to and better, to play with. Find workshops and small concert venues. You can improve somewhat on your own, but you'll get further faster if you have other musicians to learn from.
I primarily play American old time music, so this is mostly tips I've learned from better Irish players than myself.
Learn to dance. When you get the dance rhythms into your feet, they will come out in your playing. If you watch musicians playing for dancing, their eyes are often permanently locked on to the dancers' feet - unless the dancers are so good that nothing can possibly go wrong!
The same principle applies to most folk dance music traditions.
1) Learn the dances, this is the best way to get a feel for any dance-based music. Not necessarily very practical though, and potentially infectious - I'm a Cotswold style morris dancer, so I tend to play all folk tunes with a hint of Cotswold morris, and I'm having to put some significant effort into modifying my style where appropriate because I don't want everything to sound like a morris tune.
2) Play along with players you like. There are a lot of things which don't really show up until you hear yourself alongside them. If you're doing this with recordings, make sure they're loud enough to be clearly heard alongside your own playing. If live, so much the better as you can watch them as well as hear them.
3) Make the tune your own. I'm not saying you should totally ignore Irish style for Irish tunes, and certainly if you don't play Irish style in an Irish session you're not going to feel very comfortable fitting in with everyone else, but folk is a living tradition and tunes take on things from each person who plays them. That's part of the point. It's possible one of the things you're hearing in the playing you want to emulate is comfort. Absolutely learn styles you like, but folk tunes move around and change a lot, so you don't have to play it precisely like a fiddler from e.g. County Clare would be expected to.
This site http://www.alan-ng.net/irish/learning/ is a tremendous resource that I found after I posted my question. It is a must read for any Celtic musician for it provides resources for listening to tunes, finding tunes, and tips for learning tunes.