It is possible to run Oblivion with 150+ mods and no crash to really speak of (except when I don't let my game breathe and try to push it too fast).
I know for a fact Oblivion is very sensitive to system bottlenecks. Meaning that you have to think about anything that may get in the way of Oblivion running - antivirus software, background job, fragmentation of hard-drive, resolution too high for your configuration, etc.
For example, I used to have a crash every couple of hours or so, until I looked at memory usage while I was playing and found out Oblivion crashed when it reached 2 Gb of memory (on XP). So I went back to optimization mods, including streamline 3.1, to try and shave as much as possible from my memory load. The result - 15 to 25 fps on an old Pentium 4 3 GHz with 3 Gb of RAM and 512 M of VRAM.... and maybe one crash every play session (not counting crash on exit).
Now, after I moved to my new Mac Pro (with 8 cores), I found Oblivion doesn't crash anymore. I used to crash on exit a lot (well... duh ! you might say). The main difference is that the new machine can handle the load of files loaded into memory a lot faster than the old one. So I tried to ramp up my settings to see if I could make it crash again and sure enough, by increasing the display resolution of the game, I went back to one crash every play session or more.
Try playing Oblivion in Window mode, at a lower resolution, with as many optimization mods as possible to reduce the load of the game on your system. Learn to 'listen' to your system and get a feel of when it is trying to catch up with you. If you are running all the time, slow down when you hear your machine is loading new areas. I installed a Fatigue mod just to get a better rhythm and force me to walk once in a while.
Let your machine breathe.