Nevermind on this, I found a solution. The thing is that addItem call was my first "real"-API method implementation with JSON parameters in the body. The former calls were authentication and getApp which is GET and doesn't have any parameters.
The problem is that Podio supports POST key-value pairs for authentication, but doesn't support this for all the calls, and I was trying to utilize single _makeRequest() method for all the calls, both auth and real-API ones.
Looks like I need to implement one for auth and one for all API calls.
Anyway, if someone needs a working proof of concept for addItem call on node, here it is (assuming you've got an auth token beforehand)
_request({method: 'POST', url: "https://api.podio.com/item/app/" + app_id + '/', headers: headers, body: JSON.stringify({fields: {'title': 'gdfgdsfgds'}})},function(error, response, body) {
console.log(body);
});