What is the standard voltage and current levels for an android battery? I am using Micromax Canvas Nitro A310; recently, I bought a new USB cable and it seems its not doing the job as required. 

My phone is not getting charged as it was before. Either it takes too long or the battery indicator not change to even 1% after being plugged on for 2-3 hours.

I am using Ampere app to check current and voltages with different USB cables and found that the one which I bought recently is showing very low current observations (230-250mA).

Need to know what are the normal ratings.
Firstly one needs to understand C-rate or charge rate. Quoting from the linked article


  C-rate is a measure that governs at what current a battery is charged and discharged. At 1C, a battery rated 1,000mAh charges at a current of 1,000mAh. In an ideal world the battery would be fully charged in 60 minutes. At 1C, the same battery discharges at 1,000mA.



Li-Ion or Li-PO (both have same charge/discharge characteristics) -typically charged between 0.5 C to 0.8 C, more often closer to 0.8 C (as a thumb rule, depends on a lot of other factors like charging algorithm,"quick charging" ,OEM specific charging protection methods etc)
Next, one has to account for charging efficiency which is typically 90% for Li-Ion chargers, so effective charging rate would be about 0.7C (=90% of 0.8 C)
Your device battery is 2500mAh as per information on net, so the charging rate in mA =0.7*2500= 1750 or less = 900 mA ( =90% of 0.5C* 2500) if your charger is charging at 0.5C (Edit OP has confirmed in comments that his charger is 1A rated, so the charging rate appears to be 0.5 C)
This is the current your app should show using standard 2A,5V wall charger (rare to find lesser rated chargers these days)
USB charging is much slower as USB 3.0 give only 900 mA and USB 2.0 gives 500mA (refer linked Wikipedia)
Current drawn for charging is NOT uniform. Li-Ion batteries go through three stages of charging of battery charging Figure 1 of Charging Li-Ion batteries- Constant Current, Saturation Charge (current decreases), Ready (almost zero current). If you plot current drawn using your app while charging a battery from 10% or lower to 100%, you would observe this. So this had to be borne in mind while measuring. As a typical example of this graph plotted on charging my phone see  this


tl:dr;

So much for theory, coming to your question:


Need to know what are the normal ratings Explanation above should have made it clear that there is no normal or standard rating being dependent on C-rate, battery capacity, charging efficiency, charging algorithm, source of charging and in which stage of charging it was measured
It is not clear from your question whether the readings are obtained while charging from a wall charger (definitely very bad if that is the case ) or from USB charging from laptop (bad)
USB cable purchased seems to be a suspect. While buying USB cables go in for shorter and thicker USB cables (they offer less resistance to current) compared to longer and thinner cables as normally available (offer more resistance to current and hence slower charging). You can always test the current using your app before buying. Alternatively Google for 24/28 awg micro USB cable and purchase that. I would suggest latter option, though more expensive but lasts across many phones you may own over a period of time (A robust Blackberry cable purchased ten years ago is still doing good)
To estimate charging time required considering all the factors enumerated, use the Battery Charge Time Calculator