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This is so dependent on reads, your image and the board, but I'll give it a shot...
First of all, I like betting draws oop, HU (or even 3-way) for three reasons 1) the flop may not have hit your opponent and you could take it down there, 2) it builds the pot if you draw does hit, and 3) you'd bet a set in this situation (and often TPGK/TPTK) so it's good for balance.
As for what to do when raised... it depends. If it's a min-raise, it's a pretty clear call b/c he's giving you odds to draw. If it's a man-sized raise from a solid opponent you should usually fold and occasionally push. Only push if there's a decent amount of money in the pot already AND you think there's a good chance he'll fold. (As a side note, you should push over a raise with a set on a drawy board too, opps will never give you credit.) You could consider calling a big raise without proper odds to draw if your opponent is bad and won't be able to fold if your draw hits, but this isn't often the case. Straights are less obvious than flushes, so you often have better implied odds with them.
In those rare cases you do call a raise... if you miss your draw, I often bet again vs. opponents capable of folding. Again, you might play a set this way and it looks extremely strong. If villain already thinks you're FoS though, be careful with this. Against a calling station or low-stakes player incapable of folding TPGK, check and hope he gives you odds to draw on the river. If you hit the draw, once again, it depends. If you have an aggro/bluffing image or villain is passive, leading is best. If villain is aggro you can c/c or c/r.
Overall, playing draws OOP sucks. It's easy to spew with them and hard to extract value when they hit. That's why I dump sc's and suited aces in EP and open them for raises in MP and later if I play them at all. And I rarely call raises with them without position.
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