I went wandering around ohiolottery.com (For instance, http://www.ohiolottery.com/Games/DrawGames/Classic-Lotto#4) and found this out:

1. The cash payoff is half the stated prize.
2. The odds to win the jackpot, as noted by the OP, are about 14 million-1.
3. The amount of money being spent on individual draws is very low. The jackpot increase was $100K for the last drawing; I don't know exactly what their formula is, but I'd be shocked if they sold more than 400K tickets for the last drawing.
4. Ohio is running a lot of lottery games; this is good for players who pick their spots.

There are also payoffs below the jackpot level, so I'm confident there's a positive EV per ticket.

The question as to how many tickets to buy, assuming you can effectively do so, is "All of them." Buy each individual ticket, take your 14 million tickets, and probably profit. (Remember, the jackpot kick will include some fraction of your 14 million, also. Plus, you'll have all the side prizes.) In practice, unfortunately, this requires a method to buy them effectively, some armored cars, and a staff of people to do it right. Failure to purchase all tickets results in some drama, for sure.

The execution expenses and risk are troubling; if those could be effectively mitigated, it's a great investment.

Assuming you're a few million short of that, though, it's harder. I buy CA lottery tickets when EV>1.20 per $1 invested. I have no strong justification for that number.