In no particular order:
If you are starting a new league with an inaugural draft, you can game the finances a bit by focusing on drafting veterans. Your initial budget and market size are determined by your payroll after the draft. The downside is that you will likely end up with a weak farm system initially, but you can try to trade away some of the expensive veterans for prospects and budget clearing purposes. Even if you can't get any decent trades, once the veterans retire you'll have a lot of budget room to play with. (I thought this might have a chance to skew things in challenge mode, but so far in testing with a real MLB league I have been unable to draft to repeat this in OOTP 18. I'm not yet sure if its because something in challenge mode prevents it, the AI drafting is better, or if I've just been drafting the wrong players).
If you are playing games out and having offensive problems, start taking pitches. You can go 'extreme' and always take pitches until you have two strikes. Or just do that for poor hitters or batters on a cold streak. Or maybe just the first time through the line up. This will help drive up the opposing pitcher's pitch count, hopefully getting him out of the game quicker. This can seem a bit 'gamey', since the AI can't easily compensate (though, anecdotally, it seemed like this was less effective in OOTP 17 than in previous versions).
Through OOTP 17 at least, the AI has been pretty weak when it comes to its reliever usage. Playing through games gives you a pretty decent advantage. To save some time, you could still sim the first 5 or 6 innings.
http://www.beyondtheboxscore.com/201...-shouldnt-they has a lot of useful advice. Sabremetric stuff may still be controversial in meatspace baseball, but following the statistics in a statistic simulator makes a lot of sense. (I haven't done any empirical testing of the tactics and strategies that I borrowed from there, but can say anecdotally that I've seen more success since I read that page).
For my lineups, I mostly follow what is stated in that link, except to rank hitters I use OPS+ instead of wOBA. I think I started this out of laziness, because OPS+ was on the view I usually used and wOBA was not. It is also an easier stat to understand, working as something of a gap between the 'traditional' stats and the more complicated stuff.
For the first ten games of the season, I build the lineup solely on ratings. After that, I primarily use offensive stats, reviewing and adjusting every ten games. If two players are close offensively, then I'll use defense to choose, and I try to be consistent about making defensive substitutions anywhere I am weak from the 7th inning on. I dislike having to take defense into account when building lineups and playing out games though, so I try to build a roster with no significant defensive weakpoints in the first place.
When drafting and down to the lesser talented options, I start drafting solely based on personality. In the past, I would create a personality view, but OOTP 18 has been kind enough to include one already. I really only care about Work Ethic and Intelligence. I'll sort by WE, then work down the list looking for the highest intelligence available (I don't think OOTP allows one to sort on two columns, that would be useful here if so). The idea is that the random talent increase stuff is supposedly based primarily on those two ratings, so it increases the chance for a 'diamond in the rough'. I've always abandoned my attempts to track if this really works before gathering enough data.
Make use of the 'team needs' trading section to find pieces you need. The quality of the trade offers I've received have greatly increased since I started using that. They still usually require a bit of work, but aren't the typical useless offers that I was used to seeing.