Resume for Software Tester position. Should I mention my previous jobs not related to IT?

Positions not related to IT sector might be mentioned in your resume under Various Jobs section. Just one line for each position is sufficient.
There is nothing wrong to skip “Various Jobs” section in your resume altogether, if you are young, but it might be necessary to mention if you are older than 40 years old.

However, avoid mentioning low wage jobs such as:

• Dishwasher
• Farm worker
• Hand packer
• Janitor and cleaner
• Maids and housekeeping staff
• Parking lot attendant
• Waiter
• Baggage porter
• Security guard
• Taxi/Track driver
• Crossing guard
• Cashier
• Laundry worker
• Fast food cook/worker
• etc.

Having said that, you should mention your previous job if it is relevant to the position you apply to. For example, one of Hitek Computer School graduates worked as a casino dealer (low wage job that involve dealing cards for games such as poker or blackjack, operating the roulette wheel, etc.). He applied for Software Tester position to the company that develops software for online gaming. His casino experience was what company was looking for! The guy did a brilliant career in QA, becoming Test Lead and eventually QA Manager of the company.