Supersymmetry and grand unification I came across this diagram in my introductory particle physics class.
Given the fact that SUSY can make the plot look suspiciously nice, what can we do with it? Also, electromagnetism has been successfully unified with weak force at TeV scale, but their 1/strength don't intersect there...So what is the importance of the intersection? Does unification necessarily require a nice intersection of the three?
 A: The idea behind this is not only drawing pretty interesecting lines; but to have a larger symmetry which includes all of the standard model (SM).
To each simple group is attached a coupling 'constant': in the SM we have three of these because $G_{SM} = SU(3)_C \times SU(2)_L \times U(1)_Y$. The values of these coupling 'constants' vary with energy and this is what your plots show. If they converge to the same value, it means that you can in principle find a simple group $G_U$ which, when broken at the unification scale, gives you $G_{SM}$.
Examples of such unifying groups include $SU(5)$, $SO(10)$, and $E_6$.
Of course, supersymmetry is not required to achieve this. But the fact that it does lead to (almost) unification without having to add anything is a very strong argument in its favor.
A: Those charts provide a way to distinguish between the high energy behavior of the Standard Model and alternatives to it and experimentally accessible energies by measuring the running of the relevant coupling constants at the highest probable energies.
A 2014 discussion of the prospects at LHC of distinguishing between the SM expectation and SUSY predictions respect to the electromagnetic and weak force coupling constants is found here. Accuracy to the percent level in the 1 TeV-10 TeV energy scale range would be sufficient to distinguish many models including supersymmetric models with reasonably light superpartners from the SM, and this should be possible at the LHC before its work is finished.
The prospects of making discoveries at the LHC by measuring the running of the strong force coupling constant are much weaker. The differences between its strength at easily attained energies like the Z boson mass, and its strength at the highest energies attainable by the LHC, which differ by a bit more than one order of magnitude, are easily calculated theoretically. 
But, the running of the strong force is very difficult to measure with high precision.
The difference between the running of the strong force coupling constant in the SM and MSSM is smaller than the differences between the running of the other two coupling constants, and the differences in the expected values of the strong force coupling constant under alternative theories are quite small relative the the precision with which the strong force coupling constant can be measured at all in a particular experiment. So, it is unlikely that the LHC will be able to use the running of the strong force coupling constant to distinguish between the Standard Model and supersymmetric models. 
The strong force coupling constant, which is 0.1184(7) at the Z boson mass (per the Particle Data Group), would be about 0.0969 at 730 GeV and about 0.0872 at 1460 GeV, in the Standard Model and the highest energies at which the strong force coupling constant could be measured at the LHC is probably in this vicinity.
In contrast, in the MSSM, we would expect a strong force coupling constant of about 0.1024 at 730 GeV (about 5.7% stronger) and about 0.0952 at 1460 GeV (about 9% stronger).
Current individual measurements of the strong force coupling constant at energies of about 40 GeV and up (i.e. without global fitting or averaging over multiple experimental measurements at a variety of energy scales), have error bars of plus or minus 5% to 10% of the measured values. 
But, even a two sigma distinction between the SM prediction and SUSY prediction would require a measurement precision of about twice the percentage difference between the predicted strength under the two models, and a five sigma discovery confidence would require the measurement to be made with 1%-2% precision (with somewhat less precision being tolerable at higher energy scales).
This is unlikely to happen at any time during the LHC's planned runs unless there is an unexpected instrumentation breakthrough in the meantime.
