Easierは形容詞です。形容詞easyの比較級ですね。
That test was easy.
That test was easier.
That test was the easiest.
More easierは間違っています。最上級のeasiestではなかったら、まだeasierです。
Easierよりeasierの場合は”even”等を使えます。
例えば、
Level 4 was easy.
Level 3 was easier.
Level 2 was even easier (than level 3).
Level 1 was the easiest.
Easilyは副詞です。
You can easily do this.
You can more easily do this.
You can most easily do this.
You can move this easily with a cart.
You can move this more easily with a car.
You can move this most easily with a truck.
英語の文法練習はこのテキスト・Understanding and Using English Grammar with Audio CDs and Answer Key (4th Edition)をお勧めです。文法の参考書は、こちらのガイド・Practical English Usageも実用的です。私も両方レッスンで使っています。