Your router must be using the following settings according to Nintendo:
WEP 64bit or 128bit with a valid key
Channels 1, 6 or 11
802.11B
Public broadcasting of the SID must be set to enabled.
Range Enhancing features should be turned off.
It is also recommended by Nintendo to change the SID of your router from the defult one. This is because the NDS connects based on the SID and two objects in the menu with the same SID can cause conflicts.
I have tested DSOrganize, Okiwi, and c|irc for WIFI and all work fine for me on both the R4 and the M3 Lite running on a NDS Lite with no firmware flashes. I have also tried DS AIM v3 and it will connect and tells me I have connected but then the "connection" screen never goes away, so the app can't be used.
As for the Nintendo USB stick, it is not homebrew compatable unless you flash the firmware to make it *act* like a router and not simply a packet forwarding device. You can easily find more information on how to do this using Google.
Goodluck,
-AW