Was 我 pronounced 'è' at some time in the past?
Your observation is brilliant. However, there's no easy conclusion.

People summarize the formation of Chinese characters into six categories, namely 象形, 指事, 会意, 形声, 转注, and 假借. For the case of "饿", it's a phono-semantic compound (形声字) made up of "食" -- the semantic part, and "我" --- the phonetic part. Therefore, you may find the prononciations of 我 and 饿 are similar. However, a phono-semantic compound does not neccessarily follow exactly the same prononciation. "我" is a ideograph (指事字), which has a more vague origin for its pronounciation.

The prononciation of Chinese characters can date back to more than two thousand of years ago. At that time, most researcher now believing, there was no tone system and the words use suffices to identify its speech, etc, like Latin does. It also uses suffices to distinguish between different phono-semantic compound words. For example in Old Chinese, the prononciation for 我 and 饿 are /ŋaːlʔ/ and /ŋaːls/ respectively(from this). It differs so much from modern days, and it developed a long way and changing from time to time. A thousand years later in Tang Dynasty, when we called the language Middle Chinese, the prononciations of 我 and 饿 changes to /ŋɑ/ but with different tones (上声 and 去声 respectively).

For 我 and 戈, they have some relationship in terms of origin. In the old days, "我" means one's own country. And country always has armies. "戈" is the arms made up long wooden stick and a metalic blade (see 说文解字). Today, we can only know that 我 and 戈 shares the same vowel in Middle Chinese, and this is related to the similar syllable coda in Old Chinese. But the root reason of the similarity is still unclear. We still lacking convinceable evidences to claim anything. Digging out the pronounciation of two thousand years without any audio documentation is a difficult thing, not to mention the prononciation system and rules.