Your AT4041s require phantom power, so you'll need something to provide it. Could be as simple as a Denecke PS-2 or other phantom power supply. There are a couple different models out there, some cheaper, some more expensive. I know AKG makes them, I think Art makes them, and there are probably others, too. I'd budget ~$100.
You're right, you'll also probably need a way to add gain between the mics & phantom power and recorder. On the cheap, you might consider a pair of line transformers to boost the signal (~$40 for a pair). These will add a fixed amount of gain and you would control levels on the R-09HR. Gear chain would look something like this: AT4041 > Denecke PS-2 > line transformers > Edirol R-09HR. FWIW, I've used the Hosa MIT-176 line transformers in the past and they worked just fine for me until I decided to get a preamp.
Given your gear, you should use the R-09HR's internal ADC because <1> it sounds pretty good on its own, and <2> since the R-09HR doesn't have a digital input, performing ADC outside of the recorder won't do you any good.