1) Plot 2 (or more) curves, and generate a composite of the two. This
composite will consist of the highest Y value at each given X value. The two
curves have different sets of X values, although they are over the same general
range.

2) Plot 2 (or more) curves and generate a curve which is the Root Sum Square of
the curves. These curves have different sets of X values, although they are
over the same general range.

Any advice or guidance on how to perform this would be greatly appreciated.

When you have two or more datasets that cover a similar X range, but with
different X values, you can use the Interpolation menu option under
Analysis:Inter/Extrapolate to generate datasets that cover that same range
and have the same X values. Supply the dialog with specific Min and Max
values as well as the desired resolution (number of points) and give the
datasets some useful name - for this example, lets call them DataA,
DataB, etc.
(Remember that menu operations usually work on the Active Dataset which is
the dataset with the check mark in the graph's Data menu.)

Once you have these new datasets plotted you can use Origin's ability to
use math operators on datasets to create new datasets. You will need to
create worksheets for the interpolated datasets:
Generate a new legend for the combined plots (Plot:New Legend)
Open the Plot Details dialog for each of the interpolated datasets
(Double-click on their symbols in the legend) and click the
Worksheet button to generate their worksheets
Give the Y column a name - B
Select View:Show X Column to include the X datasets
Add a new column to the DataA worksheet (C)

Now in the Script window (under the Window menu option), you can type:

dataa_c=dataa_b>datab_b?dataa_b atab_b

This statement compares the DataA_B column to the DataB_B column and puts
the larger value in the DataA_C column. This statement would need to be
replaced with a short script to handle the situation of three or more
curves.

Or you could type:
dataa_c=sqrt(((dataa_b)^2+(datab_b)^2)/2)

Which (if I recall my math correctly) will give you the RMS value - modify
it for the Root Sum Square requirement.