DHT22 bad readings on long rj45 cable
Your sensor isn't meant to drive meters of cabling. That's simply not what it was designed for.

The idea to use Cat6 cabling is good, and I can see that it comes from the realization that ethernet over such cable works over long distances, too.

However, in ethernet, the twisted pairs of the signal lines are driven differentially (i.e. the current on one conductor is the opposite of that on the other, and at the receiving end, the difference between potentials is evaluated), and great care is taken to ensure the signal is robustly read and reconstructed.

Your circuitry has no measures whatsoever to fulfill the same role, so it simply doesn't work over a long distance of cabling, where you simply lose a lot of voltage to ohmic drop over distance, where you get the full length as antenna or secondary winding to a parasitic transformer with the power grid, and, most importantly here, where you take no steps to help the transmitter drive the capacitive and inductive load that the long wire represents.

For this to work, you'd need to change a few things:


long runs of twisted pair really aren't good for low-voltage power transfer. Use transformers to step up your voltage at the feeding end, and step down at the receiving end. 
You'll need single-ended-to-differential conversion at the sensor end, and the opposite at the receiver end.
You'll need to match the impedances.
Not quite sure what the voltage divider in the sensor's data line does – but it does look to me like unnecesary load to the sensor. However, this will be obsolete by itself when you use the differential transceivers
I don't know what speeds you need from the IR transmitter – but it was a good idea to use something to increase the drive strength of your Pi. However, instead of using a transistor at the transmitting end only, you'll want a schmitt-trigger buffer + drive transistor at the receiving end, or go for differential transceiver  + driving transistor right away
This all considered, it's usually simpler to go and have a small microcontroller at one end of such a long line that does all the local interfacing, and only needs a single link over the long distance. If you go that route, you could probably even just use I²C instead of differential transceivers; low-speed I²C is relatively robust, and all non-least-cost microcontrollers come with I²C masters integrated, and the Pi can also act as I²C device; there's even kernel drivers.
If you want to try I²C: there's actually sensors other than the slightly underdocumented DHT22 (where do people even find these things?!) that speak I²C themselves (example temperature sensor, example humidity + temperature sensor). That would save you quite a bit of trouble, as you could, without any further ado (actually: maybe a pull-up resistor) attach that thing to the Pi.
If you actually want to do it like the "big kids": Industrial sensors typically are just supplied with a constant current (somewhere in the 4–20 mA range), and you'd read out the value by the voltage drop across sensor + cabling. Current loops are insensitive to cabling resistance.