I have Google spreadsheet with script attached to it (with the Tools->Script Editor tool).
I want to call one of script function from external Android App. Is it possible? Should I use Spreadsheet API?
Unfortunately, you cannot directly call your script from any external application.
However, you can change it to be a web application, then invoke it via an HTTP GET or POST from almost anywhere, including an Android app.
Insert new rows into Google Spreadsheet via cURL/PHP - HOW? provides an example of a web app that you could adapt.
Should I use Spreadsheet API?
Your question doesn't actually say what it is you want to do, so the answer is "it depends". You still won't be able to invoke an embedded script using the Spreadsheet API, but you will be able to read and write spreadsheet content.
Obviously the answer depends on your usecases, but have you checked the Google Appscript API? As stated it
provides methods to remotely execute Apps Script functions