What's the best way to scrape & paint exterior wood window casings ?

consider power washing them, it will take all the loose paint chips and all off and some of the harder, then you can hand sand the rest much easier

The best is not always the easiest, but hand scraping and sanding is usually the method. Power washing the casings can also work, but a lot of water is used and the paint chips go flying. There are solvents that can be used as well.

Protect yourself with a dust mask and some gloves to prevent blisters.

You can scrape away all the loose stuff and then paint it with a thicker paint/primer like XIM Peel Bond which fills in the cracks and divots and is probably less expensive and time-consuming than scraping down to bare wood. Pros use tricks like that on the second stories to cut down on the cost.

An oil-based primer that gets a chance to slowly dry and soak into the wood will probably be your best bet.

Pressure washer ...careful to not break glass...then elbow grease. Paint stripper works but its messy.

Scrape lightly with a wire brush (you don't want gouges) or use a paint scraper (better). Make sure any caulk that may be overlapping the casing is paintable, otherwise it will repel the paint. Use an EXTERIOR high-adhesion primer and paint.

http://thecraftsmanblog.com/choosing-the-right-primer/

https://www.benjaminmoore.com/en-ca/interior-exterior-paints-stains/product-catalog/fspep/fresh-start-premium-exterior-primers?gclid=EAIaIQobChMI2IDPyMrL1gIVDC1pCh1nWwaREAAYASAAEgLkR_D_BwE&gclsrc=aw.ds

http://www.homedepot.com/p/KILZ-1-gal-Adhesion-Bonding-Primer-L211101/204763136