After 17/18 months employment can you be terminated without written reason, cause or record of employment? Is serverance required by law if record of employment has not been provided and employment insurance is unavailable?

An employer does not have to provide a reason but MUST pay severance. The only way an employer does not have to pay severance is if it has "just cause". This means that the employee did something truly awful. An employer also has to issue an ROE, regardless of the reason for termination. You are very likely owed severance which could be worth a few months of salary. It is important that you give us a call to discuss.