I'm thinking of moving to Nana somewhere between the area of Soi 4 and Soi 11. Are there any big-box stores like Tesco or big C around?

Tesco is a couple of stops east on the BTS, or Big C a couple of stops west on the BTS, or go north on Asoke, or farther on MRT, Phra Ram 9. 

 

For food, there is Foodland and Villa in Ploenchit Center nearby.

 

Both brands have locator pages on the internet.

 

Darn, that's the answer I was hoping not to hear. Currently I live on Sukhumvit 22  and there is a big C and Tesco within a 10 minute walk from me (on Soi 26 I believe)

Not within quick walking distance (I don't think). But there is a huge Big C across from Central World, Chit Lom BTS stop.

Anyone know of any good "small box" general purpose stores around Nana?

Go to the Post Office near Soi 4 on Sukhumvit.

If you are on Ekkamai BTS and look against Nana take the end of BTS pointing againts Nana and this road on right side, max 10 minutes walk is a Big C. Also if interesting for you I am sure you also find a Index with stuff.for your Apartment. The biggest Big C I have been in, is near Central World. Go to Sitlom BTS and walk from there on the Skywalk to Central World and just opusite CW you see Big C.