First off, you're right in that picking up an Olympus, even if things were to go sideways and the DSLR business were to shut down, you could still get lenses for many years to come on the used market - so as long as the camera could serve your needs, you were happy with it, and you didn't have any upgrade body needs, a person could shoot for many happy years with an out-of-production camera or brand. Just make sure you research the camera, make sure you like it, and that the lens availability now and in the future won't be a worry. And for now, Olympus is still in the game.
Secondly, you asked about articulating screens, and received some mention of the available Canon 60D or Nikon D5000. To add to that list, take a look at almost any Sony DSLR as tilting screens have been one of their big features for many years now - the A500, A550, A560, A580, A33, and A55 of the recent models all have tilting LCD screens. These also all have the only truly usable live view systems of any DSLR - as they can shoot with full phase-detect autofocus and with no shutter delay. Like Olympus, they have in-body stabilization, and have backwards compatibility to another defunct brand - Minolta. All Minolta Maxxum/Dyxum lenses will work normally on Sony bodies. The sensor in the A500/550 and A33 is the same as that in the Pentax KX, Nikon D3100, and D5000. The sensor in the A580 is the same as in the D7000 and Pentax K5 (Sony makes most of the sensors for both Nikon and Pentax).
In the end, the brand doesn't much matter - and I know some photogs still shooting with Minolta bodies who take better photos than some folks picking up brand-new high-tech Nikon D7000s. The camera brand won't make you a good photographer - it's just a tool. If you are fully aware of Olympus' focus lately on their Micro 4:3 line rather than the DSLR line, and that they may or may not continue DSLRs in the future, then as long as you're happy with it, go for it. Otherwise, certainly consider what's available from Sony, Canon, Nikon, and Pentax too.
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses