How can I diagnose slowness in an Android device? In Windows PC, when some computer is very slow, I use software like SysInternals Process Explorer to check background programs that is using more CPU/RAM. I use SysInternals AutoRuns to disable auto start programs too. 

In android device, what tools/procedures can I use to diagnose this kind of problem?
I don't think you'll be able to control start-ups but you can surely monitor CPU usage. Open Settings>Developer options - and under Monitoring section enable Show CPU usage. CPU usage and processes will be shown as overlay on screen. Also there are number of apps in Play Store to serve the purpose.