consolidate and relationships help - excel 2013

Greeting genius people,

I'm trying to solve a problem in a much simpler way than I know how to do. The basics are:

1. I have multiple tabs (83) with similar formatted tables (same column headers but different numbers of rows).
2. I have one sheet that I would like to combine three columns of data from each of the tabs (same three columns on each tab).
3. I want to omit any rows of data that are blank in all three columns.
4. I need the combined data to be live - so I'm staying away from Pivot Tables...I need changes to be seen without needing to hit a refresh button.

I am running Excel 3013, but I'm an early adopter, so many of those using this workbook will be using 2010...I doubt that anyone is still running 2007, but it is a small possibility.

I know that I can create VLOOKUPS to do this, but at over 80 tables with anywhere from 10-30 rows of data, I am horrified at developing the formulas when I think that the new updates in 2013 might be able to do it for me much easier.

I have not used relationships before and I have no idea how to consolidate. My feeble attempts thus far have included error messages stating there was no data to consolidate (which is wrong) and the time I have already invested in trying out something new is beginning to make me want to give up and just write each of the 1500 plus VLOOKUPs.

Does anyone have any suggestions or tutorials they could steer me toward?

Jerry - I had planned to put a running overall total on the top of each tab.
With your ideas, would the grand totals and a GETPIVOTDATA formula on each sheet actively refresh if they place data in any of the columns I am trying to gather data from?

Ford- my difficulty is that non-tech savvy folks will be using this as a budgeting tool for next year. There are several (17) large categories of spending with 5 minor categories beneath each...and each minor category has 10-30 specific budget lines. No one will use every line, but they may decide to create an outlay of funds next year on a line they haven't used in the past two years.

I'm trying to fix it so they can get an at-a-glance summary of each of the large-minor combos but keeping an overall total for the entire thing.

Does that make any sense? would it be helpful to upload a pic or some dummy versions? I haven't created each tab possibility yet, but I have a file that holds at least 4 major categories and their 5 minor summaries each.

Ford - where would I place this formula? Would it bring all three columns I need if I just copy it in each column? It's more advanced of a formula within a formula than I am used to!

What is the C794 reference for in the formula above? I've entered it into my summary sheet, but I'm getting the REF error. I noticed that the autofill in the column increases that value as it continues down...so it ends up circling around to look back at the column for a criteria...