You can use free easeus partition manager to mess around with your partitions. Be sure not to change the current Win 7 main partitions, which are the second and third partitions currently. Now your major problem of why Win98 does not see any partition to install on is because currently there is no suitable partition!!
For Win98se you must
not have dynamic partitions, you must
not have NTFS formatted partitions.
Study this
http://msdn.microsoft.com/en-us/library/windows/desktop/aa363785(v=vs.85).aspx
You could use a partition manager to shorten the third and/or fourth partitions to release about 5Gb of unpartitioned space. In that empty space you then create a primary partition for Win98se and format it FAT32. You need to be able to set this partition as the active partition when you boot into it, and there can be only 4 primary partitions per standard HD. This means you may also have to convert the current DATA partition to an extended partition.
However, your main problem is that Win98 knows nothing about any of the partitions you currently have, nor anything about the Win7 OS. Only when Win7 is actually installed
after Win98 will it be possible to dual boot using the standard booting facilities of a Windows OS.
You will need to get round the booting problem by using a package called EASYBCD which will be able to adopt your existing BCD store which boots Win 7 - probably from the second partition, and add the link to boot Win 98 through it's now very old-fashioned method of two files, IO.SYS and MSDOS.SYS which will fire up the two other files which define how your OS starts up - CONFIG.SYS and AUTOXEC.BAT
Other problems you will probably hit are that Win9e will not run at all on many modern PC's because they have
too much memory. There are means within config.sys or autoexec.bat to force Win98 to only use a maximum or 256Kb of memory, but I've found these things often wont work.
As you can see, there are flaming hoops by the handful to jump through, and unless you have a good deal of experience, my strong recommendation is to forget the idea - get an old PC instead.