(1) Simmons is barely better against ies than Singleton and against righties, it's a no-brainer.
(2) In general, I believe the main thing with lineup is to get your best hitters at the top of the lineup, and it doesn't matter too much after that, but generally my philosophy is as follows.. #1 should be a hitter more slanted toward OBP with a lower ISO as he will come up with nobody on and no outs way more than anybody else, obviously. Number 2 should have strong OBP and, if I have speed, I will put it here to cut down on the double plays. Number 3 should generally be the worst of your top-5 and be a lower-OBP, higher power guy as he is often up with 2 outs and nobody on. Number 4 should be another higher-power guy, and, all things being equal, your best hitter as they will be up with men on base more than anybody else. I generally have #5 be a better hitter than #3 but not always. After that... just best hitters in order.
So for your team, I would say:
(1) Simmons/Singleton- Simmons isn't ideal, but you really don't have any great OBP guys in your lineup. Since whoever you play at 1B will be among your 3 best bats, I would bat them leadoff to get more ABs.
(2) Andujar- His speed will help avoid double plays, and decent contact-eye combo will give him a decent OBP. I would think about swapping him with Walker against ies though.
(3) Walker- Probably our third best hitter and he slants more toward power than OBP, so he's a good fit for #3.
(4) Tanaka- Your best hitter and best power hitter. I would bat him cleanup.
(5) O'Brien
(6) Wallace- O'Brien's a bit better against righties, Wallace is a bit better against ies, I don't think it makes a huge difference where you slot them.
(7) Everett- I'm not a huge fan of high-split, low-contact/power guys.
(8) Pitcher- Most lineup optimization stuff suggest there is a slight advantage to batting your pitcher 8th
(9) Woo- Clearly your worst non-pitcher