The 3.3volt supply of a Nano is extracted from the USB<>Serial chip, and 30mA draw is about max.
It will not reliably power a regular rf24 let alone the high powered ones. Try putting a 10uF cap across the supply to the radio, as close as possible to the radio. Try using a 2 AA cell battery pack to power the rf24 (connect the battery ground to Arduino ground). I use homemade adapters with a dedicated 3.3V regulator for each radio (probably like the ones that you have on order).
A couple of other things that helped me:
If using the high powered radios make sure to separate them by a few meters. They may not work too close together. Try the lower power settings.
Reset the radios by cycling power to them after uploading new code. I have found that to help. They do not reset with the Arduino.
There is a lot of good information in the simple rf24 tutorial by Robin2.
If you post the transmit code I can test the code with 2 Unos and rf24 (low power) modules.