When we do our hurricane season whirlwind tour of the States each summer/fall, we always take our "main" ukes (a concert and a tenor in separate gig bags). Modes of transport typically include boat, dinghy, golf cart, car, and bus, not to mention numerous flights. We've even taken them with us on an ATV. We stay at hotels, motels, b&b's, rental cabins, time shares, and with friends and family during that time.
On flights, our carry-on luggage consists of concert uke, tenor uke, cat (in mesh carrier), and backpack. Rich stows the ukes overhead (and keeps an eye out for other people putting their luggage overhead). The cat and backpack go under the seats in front of us.
I take my Risa stick in my checked bag, and we have also travelled with our Eleukes in our checked luggage. We've never had a problem anywhere, although TSA is always very suspicious of my harmonicas...