Let's start with some basic search methodology. The idea here is to "read" through a log-file and search it for specific terms. You can use grep by itself or sed, awk, gawk or a dozen other commands. If you use a Linux workstation or the windows ports of Linux utilities it will look something like this:
grep -i "keyword" -r *
If the output doesn't look the way you want it to or you are having trouble targeting specific files with grep alone, you can refine somewhat by stacking commands like so:
Strings -s *.log |grep -i "keyword"
I guess the big secret here is the keywords. They will vary slightly from case to case but, generally speaking, SQL injection can be identified by searching for union select, xp_cmdshell, concat and also by looking for specific database table names in the logs. The last of these is especially true if you know what type of data is at risk and where it resides. One of my favorite PCI related searches is to look for "cvv" in the logs or "cc_number". If you are concerned about data being snatched from a particular database, grab the table names and run a search. It's very common to see fields like "First_Name, Last_Name, Address"
OUCH!