Sorting the time format in shell script

Maybe not super elegant, but straight forward in Python:

#!/usr/bin/env python                                                           

import operator

# 1 month = 28-31 days and 4 weeks = 28 days, so month is kept separate
time_in_seconds = {
    'week': 7*24*60*60,
    'day': 24*60*60,
    'hour': 60*60,
    'minute': 60,
    'second': 1
}

if __name__ == '__main__':
    times = []

    with open('sample_time.txt', 'r') as f:
        for line in f.read().split('\n'):
            months = 0
            seconds = 0
            try:
                for pair in line.split(', '):
                    num, denum = pair.split(' ')
                    if denum.startswith('month'):
                        months += int(num)
                    else:
                        seconds += time_in_seconds[denum.rstrip('s')]*int(num)
                times.append([months, seconds, line])
            except:
                pass

    sorted_times = sorted(times, key=operator.itemgetter(0,1))
    for line in map(operator.itemgetter(2), sorted_times):
        print(line)

It assumes your file is called sample_time.txt.