Earthly means of or relating to the earth, especially as opposed to heaven; worldly.
Usage Example: His affinity to all earthly things was apparent.

Earthy means of, composed of, or characteristic of earth.
Usage Example: She decorated her drawing room in earthy tones.

Eave means usually, eaves the overhanging lower edge of a roof.
Usage Example: The tree swallows and the barn swallows had built their nests under the eaves of the farmhouse.

Eve has the following meanings:
1. It can refer to the day before.
Usage Example: They all assembled on the eve of her departure.
2. The period preceding or leading up to any event, crisis, etc.
Usage Example: People were confused on the eve of the Civil War.
3. The latter part of the day (the period of decreasing daylight from late afternoon until nightfall).
Usage Example: She toiled away from dusk to eve.

Either means one or the other of two.
Usage Example: Either I heard it wrong or what he said was not true.

Ether is a colorless volatile highly flammable liquid with a characteristic sweetish odour, made by the reaction of sulphuric acid with ethanol and it is used as a solvent and anaesthetic. 
Usage Example: On external application, ether evaporates very fast, producing intense cold.

Elegy means a mournful or plaintive poem or song, esp a lament for the dead.
Usage Example: "Lycidas" an elegy for Edward king on was composed by Milton on his death. 

Eulogy means a speech or writing in praise of a person or thing, especially a set oration in honor of a deceased person.
Usage Example: There was hardly anyone in the crowd who remembered the name of the person giving the eulogy.

Elicit means to draw or bring out or forth; educe; evoke.
Usage Example: Despite her best efforts she has been unable to elicit any aid for the animal shelter.

Illicit means not legally permitted or authorized; unlicensed; unlawful.
Usage Example: He felt happy at having smuggled an illicit bottle of water in the auditorium as the venue was selling them at exorbitant prices.

Licit means legal; lawful; legitimate; permissible. 
Usage Example: The video footage was licit and clear.

Eligible means meeting the stipulated requirements, as to participate, compete, or work; qualified.
Usage Example: His percentage made him eligible for a number of scholarships.

Illegible means unable to be read or deciphered.
Usage Example: The cashier at the bank refused to cash the old lady's check as her signature had become illegible.

Ineligible means not eligible; not permitted or suitable.
Usage Example: The employees of the firm were ineligible for the contest.

Legible means capable of being read or deciphered, especially with ease, as writing or printing; easily readable.
Usage Example: The photocopies of the report were not legible.

Emanate means to issue or proceed from or as from a source.
Usage Example: The room was filled with the fragrance emanating from the flowers.

Eminent means high in station, rank, or repute; prominent; distinguished.
Usage Example: The most eminent of lawyers and statesmen were present at the meeting.

Immanent means remaining within; indwelling; inherent.
Usage Example: We were mesmerized by the immanent beauty of the river and the deep forest behind it.

Imminent means likely to occur at any moment; impending.
Usage Example: The danger to life though imminent still the power of prayer kept our hopes alive.

Emerge means to come forth into view or notice, as from concealment or obscurity.
Usage Example: The ship could be seen emerging from the fog from the lighthouse.

Immerge means to plunge, as into a fluid.
Usage Example: The boat was immerged in the rising waves.

Emigrant means a person who emigrates, as from his or her native country or region.
Usage Example: He sailed from England to America on an emigrant ship.

Immigrant means a person who migrates to another country, usually for permanent residence.
Usage Example: After the Second World War, immigrants could not find work easily.

Emigrate and Immigrate are the verb forms of the above discussed words.

Endemic means natural to or characteristic of a specific people or place; native; indigenous.
Usage Example: The disease endemic to the tropical region has affected almost a hundred people.

Epidemic means a temporary prevalence of a disease. 
Usage Example: It is getting difficult to control an epidemic of Horseweed even with herbicides.

Pandemic means prevalent throughout an entire country, continent, or the whole world; epidemic over a large area. 
Usage Example: A pandemic of fear has spread among the political parties before the midterm elections.

Inquiry refers to a specific search or examination of facts. It is mostly used for official investigations.
Usage Example: The police carried out an inquiry into the murder case.

Enquiry refers to a general request for information. It can also be used for a 'search for knowledge in a particular field of study'.
Usage Example: You should make an enquiry about the train schedule ahead of your travel.