SUMIF and VLOOKUPS Combined May be the Answer?

Hello, I was wondering if anyone would be able to help me with an Excel problem I am having.

I have a large Excel workbook which contains around 40-50 seperate spreadsheets, each of the spreadsheets holding information about a different project, I also have a front sheet which rolls up all the basic project information. However what I am trying to do now is a little bit more complicated.

I have created a Spreadsheet entitled Budget Codes which contains all the different budget codes which could be used to purchase something against an order for a project. In this spreadsheet I have 'Budget Code' 'Amount Allocated' 'Amount Spent' and 'Amount Remaining'. What I want a formula to do, is to look into the order lines of ALL the other project sheets, identify where a particular budget code is used, and where it matches the code in the respective cell to add the value of that order, thus totalling all the orders placed against that project code...where there may be multiple order lines, if this makes sense.

If it doesnt (because I am not great at explaining), I need a formula to look up where the budget code in one cell matches the budget code in multiple other cells and then know to look at the value/amount on the same line as the project code and them all up together. I am thinking that SUMIF and VLOOKUP may be able to help me but at the moment I feel like I am banging my head against a brick wall.

If anyone is able to help I would be exceptionally grateful.