You can use DOS commands to copy them, but mIRC can also copy files into each other with a bit of scripting.
DOS sounds faster, just use the format...
COPY logfile1 + logfile2 + logfile3 outputfile
Use the + between each file to add, and end with your output file just a space separating the last file to add.
You should be able to use /RUN to execute the copy commands. Failing that you can use /write to create a batch file and /run the .bat file.
If you want to create a script, check the following help section with: "/help file and directory identifiers"