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I like the bet/call a lot more than check/call.

For the bet/call, if villain raises every time he has a straight, we lose 2 BB. On the other hand, we win 1 BB if he doesn't have it. I'm arbitrarily setting villain folding 10% of the time. I'm not taking into account getting raised by a lesser hand for simplicity. Also I'm assuming villain will raise with a straight, which makes sense.

Let p be the probability of villain holding a straight.

p * (-2BB) + (0.9-p) * (+1BB) + 0.1 * (+0BB) > 0
-2p + 0.9 - 0.9p > 0
0.9 - 2.9p > 0
1 > 2.9p
p > 0.345

Villain needs to have a straight more than 34.5% of the time to make a bet unprofitable. I believe villain will have a straight less than 34.5% of the time, so I bet/call based on the EV calculations.

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For the check/call, villain is a lag. Does this mean he will bet anything when checked to? I'll set the probabilty of villain betting a lesser hand to 25%, meaning 75% of the time he'll bet when we're beat. I'm unsure on these values I used here, some input would be great.

0.25 * (+1BB) + 0.75 * (-1BB) = -0.5BB

That was easy. Check/calling is -EV if villain is value betting over half the time with a hand that beats us.

This seems to go against the norm of check/call replies, I'll be double checking this.

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When we win with check/call we win the whole pot, not just some part of a BB.

True