At this point, your employment verification doesn't seem like the biggest issue. The ECO even put it at the end after the "your application has therefore been refused" line.
Your history with UK Immigration and your bank balance are significant issues right now. You have an overstay on your record and further hurt your credibility by failing to disclose a conviction. This already hurts your chances substantially, so any hope of a successful application needs to be rock solid. But you've submitted a bank statement showing a closing balance of £8.61. At that point, it's over; the ECO is going to look at that and not be comfortable you won't overstay in the UK. Even though your employer is paying toward the cost of the trip, your personal circumstances help demonstrate that you'll return home to Nigeria, and you haven't demonstrated that.
You can address the employment verification issue by making sure your employer is able to handle a simple telephone call, but there's no point in considering reapplying until you have a solid financial history to provide. Please read Should I submit bank statements when applying for a UK Visa? What do they say about me? for an idea of what they're looking to see. Incidentally, this will also help verify your employment: a regular history of salary deposits on your bank statements demonstrates that you're employed, paid as you've stated, and are living within your means.