It's quite a bit of work, but you probably want to use the axes command. A figure window can host any number of axes, where each axes has it's own position, data, annotations, color etc.
The most difficult thing for the application you describe is that each axis position needs to be defined in the coordinate frame of the underlying figure, which means that some math may be required to create the illusion that the axis is correctly positioned within a parent axes/
For example, if you first create a simple plot
figure(1234); clf;
plot(1:10, rand(1,10),'.k-','linewidth',5);
xlim([1 10]);
ylim([0 1]);
set(gca,'color','y'); %This just helps demonstrate the next steps
You can place another axis directly on top of the first, and then
ha = axes('position',[.2 .3 .1 .1])
plot(linspace(0,2*pi,100), sin(linspace(0,2*pi,100)), 'b-')
xlim([0 2*pi])
You can adjust the the properties of the inset axis to suit your particular needs, for example
set(ha,'color','none'); %A transparent axis
set(ha,'xtick',[],'ytick',[]); %Remove tick labels
title(ha,'This is an inset plot')