All oils that are classified as emmenagogues should be avoided during pregnancy, as they stimulate blood flow to the uterus and encourage menstruation.
Jasmine is not only an emmenagogue but also a parturient and uterine tonic. Parturient oils promote labour so should definitely be avoided during pregnancy.
The ONLY oil I use on pregnant clients (unless they are 40 weeks) is Mandarin because it's very safe (it can also be used on kids), and it's very nourishing for the skin so it's great for stretch marks.
As far as using oils in labour goes, Jasmine, Rose and Lavender would be my top choices. However, I support women in labour and have only used aromatherapy a couple of times as I don't believe it's 'necessary' and neither have my clients. I don't even bring oils with me.
The one thing I do keep in my birth bag is a 100ml glass bottle with a spray attachment that can be used as a spritz during labour to refresh the labouring mum (who usually gets very hot). In it I put 10 drops of Lavender, 15 drops of Peppermint, then fill it up with filtered/bottled water. Shake the bottle a bit before each use to disperse the oils, otherwise they'll float on the top.
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HTH!