Assuming that what you mean is that your Spreadsheet has 3 columns, and in
each row, one, two or perhaps even all three of those columns could be blank
/and/ it is OK simply to start checking with the first column and move to
the next as you say, what you need is something like

{ IF "{ MERGEFIELD column1 }" <> "" "{ MERGEFIELD column1 }"
"{ IF "{ MERGEFIELD column2 }" <> "" "{ MERGEFIELD column2 }"
"{ IF "{ MERGEFIELD column3 }" <> "" "{ MERGEFIELD column3 }"
"some other value if all three are blank?" }" }" }

This can all be on one line, but all the {} need to be the special field
braces that you can insert using ctrl-F9 - you can't just type them on the
keyboard. Everything else is plain text. I include the spaces and quotes
partly because that's the way Word usually does it, and partly as a
defensive programming strategy, but many people would drop quite a few of
them.