Yes Woodlawn itself is perfectly safe. I live in the neighborhood, but I'm Irish-American, not Irish. There is a big Irish immigrant community in Woodlawn along with a large number of Irish-Americans.
There's good craic in this neighborhood, lots of pubs/bars, a dancehall, Irish restaurants, a chip shop, everyone has a good time. Work is pretty easy to find. Construction is the favorite job of guys who move here from Ireland. The companies will train you and I believe the pay is $200 a day. The other big job for Irish guys coming over is bar tender, lots of those jobs down in Manhattan.
The rent is also pretty cheap here for the NYC area. You can share an apartment and rent a room for around $500 a month or get your own place for $900/$1,000 a month.
The subway is also pretty safe, but you do have to stay alert so that nothing happens. The 34 bus runs down Katonah ave which is the main strip in Woodlawn and takes you to both the 4 (runs down the east side of Manhattan) and the D (runs down the west side of Manhattan). We also have a Metro North Train station in Woodlawn which has commuter trains. This is very popular, but more expensive than taking the subway.
If you are planning on working construction though I wouldn't worry so much about transportation as most Contractors will pick you up and drop you off with their truck. For a bartending job I suppose you're going to have to get there on your own.
The Governor of NY just changed the state policy recently so that in 6 months you should also be able to get a car if you don't have a ss#, but in Woodlawn a car isn't really necessary unless you want one.
Check out the classifieds in the Irish Voice:
Irish Voice Newspaper Irish Echo Online for more info.
Send me a PM if you have any other questions.