How much energy would it require to get the ISS around or on the moon? And how much fuel would that require? And how many cargo missions would that require? And if that is not worth it, would it be beneficial to disassemble the ISS and transport the useful parts to the moon?
Since you ask several progressive questions, ill try to give you a progressive answer. Going to the moon with the ISS and landing it are 2 completely different topics, therefore I will focus in getting in a Lower Lunar Orbit (LLO)
How much energy would it require to get te ISS around the moon
To go from a Lower Earth Orbit (LEO), in which the ISS resides now, to a LLO requires a delta-V budget of roughly 4.04 KM/s. This consists of 2 parts, accelerating until we reach an lunar transfer orbit and then decelerate unit we are in an orbit around the moon. The latter of the 2 cost roughly 840 m/s, whereas the transfer burn is roughly 3200 m/s.
How much fuel would that require
Rocket engines efficiency is rated in Isp. In short, the higher the Isp the more efficient a rocket will propel you. The amount of fuel required is therefore related to the Isp of the rocket used to propel the ISS. In the next section I will give some Isp examples and the required amount of fuel.
A simple calculator to try for yourself can be found here.
How many cargo missions would that require
To get to the moon we want to accelerate the ISS, but in doing so we also accelerate the fuel that it is caring. Since the amounts of fuel are massive, it would be more probable that the ISS would be supplied with fuel, burn on its periapsis and then be resupplied to do another round. It does need to be able to decelerate when it reaches the moon. To incorporate this in the calculations I have taken the weight of the ISS as 420000 kg, except for the last LEO burn, when it also carries the weight of 840 m/s worth of fuel.
Currently the ISS requires some delta-V to maintain its orbit, which is being provided by an ATV. To give you an idea, we will first look what happens if we would use those. The ATVs used have 4.7 tonnes of propellant and an Isp of 270s. This gives it a delta-v budget of a whopping 29 m/s. This would require 110 trips with a burn in LEO and another 33 that have to be used to provide fuel to decelerate at the moon, giving a total of 143 trips. Of course a these also carry a lot of supplies and with 143 trips instead of the normal annual trip we could expect that it would be entirely filled with fuel. If we look fill the entire cargo area this would provide 12 tonnes of propellant. (cite) This would reduce the burns in LEO to 43 with 13 to supply the ISS with braking propellant. But with a total of 56, this is still a lot.
Instead of using the existing propulsion system one with a better Isp could be designed. Where the ATVs have only an Isp of 270, an higher Isp engine could be used. For example the Centaur with an Isp of 450s, would require a lot less fuel. With the largest payload to LEO at this moment being 28790 kg using the Delta IV, we would only need 18 burns in LEO and only 3 cargo ships to supply the braking propellant.
Note however that I did not include the weight of the fuel tanks required to store the braking fuel in the ISS, so this will increase the amount of propellant needed.
If it is worth it?
Of course this question also has a financial side, therefore I calculated the amount of trips it would take to use SpaceX Falcon Heavy, which with a price of 2200 $/kg is, according to this topic is the cheapest per Kg to LEO. (Although it isn't available yet). For the record, with 63800 kg to LEO and a Isp of 311, it would require 7.5 burns in LEO and 2 launches to supply the braking propellant.
Summing up to a total of roughly 607.000 kg of propellant to be supplied to the ISS at a total cost of 1.3 billion dollars.
In my own opinion I would say no. Although this is only 1% of the cost of the ISS as is, a lot of the compartments that we have now are simply not needed at the moon. It might be worth it to take one or 2 single modules, but with the technological advancement it might even be better to take new and improved equipment.