Supercollider? I 'ardly know 'er!
This comic refers to the first startup (turn on) of CERN's Large Hadron Collider (LHC). There was a theoretical concern that that the LHC experiments could create a black hole that would suck in our planet.
Cueball uses this concern when telling Megan that this could be their last night on Earth, but since the scene is in a bar, this is just another lame entry he uses because he just wants to spend the night with her.
Megan answers as a physicist and explains that, first of all, they will not start colliding particles just because they actually turn on the collider. That will take a while, during which everything needs to be checked. Secondly, scientists have determined that the fears are unfounded — among other things because cosmic rays have already been bombarding the Earth with particles even more energetic than those created by the LHC. Thus, if the LHC could create a black hole that would suck up the Earth, then that would have happened long ago due to the cosmic rays. (At present time, the collider has been colliding particles for years, and if you read this line on or near Earth, then the Earth is still here; if you read it in a galaxy far away from the Milky Way, then it is somewhat more plausible that Earth may have been destroyed in the time that the signal took to reach you — although not necessarily by the LHC.)
Cueball feels rejected by her answer and turns away to leave her, but she calls him back explaining very directly that she did not say "no" to his request (to try to stay a night with her). Also, as she is a physics grad student, she needs an excuse to party — the excuse being that the LHC is turned on.
Cueball feels encouraged and continues his attempt to get her in to bed. But in his next sentence, he unwittingly uses three of the six quark flavors (up quark, charm quark, and strange quark). Megan continues to be very direct when asking if she has to be on top or bottom (when they are going to have sex). But this is also a sentence she chooses so she can continue using quark flavors (top quark and bottom quark). Cueball is flustered and complains that she is assuming too much, since he hasn't even bought her a drink yet. Megan then makes it even worse when she makes an order of two whiskey sours straight down — to use the final flavor (down quark).
Maybe she just teases Cueball (with her knowledge about the LHC and quarks), or else she is actually so turned on by the LHC Turn-On that she wishes to have sex with Cueball as soon as possible.
The quarks are some fundamental particles the LHC is generating. All six flavors of quarks are in the last panel: up, down, top, bottom, charm, and strange. They are also referenced in 1418: Horse, 1621: Fixion, and in 1731: Wrong, the latter also mentioning the up and down flavor. The mention of the drinks being served "straight down" is a reversal of the common bartending term "straight up," but there is no "straight down" in bartending.
The title text is of course a very old joke "I 'ardly know 'er!," which was referenced in 259: Clichéd Exchanges. In this case, Supercollider (another name for the LHC) should be misunderstood as "(Did you) Supercollide her?", which you could put into a (nasty?) sexual context. Using this sentence at the wrong moment could be bad for a nice romance. This could be a reference to the Futurama episode "That's Lobstertainment!," in which Humorbot 5.0 tells a similar supercollider joke.