I must dissent from Maulik V's statement that an ordinary person is one who does not have a quality that you “expect”. On the contrary, an ordinary person has exactly the qualities you expect in everyone, no more, no less.
In any case, ordinary has (ordinarily) no offensive connotation, unless you are specifically denying someone some excellence he has claimed to possess—and in that case the offense lies in the denial, not in the term ordinary.
Yes, and that's in fact what "immortal" mostly has meant.
The etymology of the word "immortal" reveals
late 14c., "deathless," from Latin immortalis "deathless, undying" (of gods), "imperishable, endless" (of fame, love, work, etc.), from assimilated form of in- "not, opposite of" ( . . . ) + mortalis "mortal" ( . . . ). In reference to fame, literature, etc., "unceasing, destined to endure forever, never to be forgotten, lasting a long time," attested from early 15c. (also in classical Latin). As a noun, "an immortal being," from 1680s.
The meaning of the word "dead" itself is
dead (dĕd)
- Having lost life; no longer alive. – Free Dictionary
When we try to compare the meaning according to the definitions of related words, we deduce that you can't. However, irregardless of antonyms and synonyms, with regards to usage, a word might have a slight meaning difference to what is implied.
Many fictitious species are said to be immortal if they cannot die of old age, even though they can be killed through other means, such as injury. – Immortality in fiction, Wikipedia
The controversy lies in the fact that being killed also results in someone's death, but someone may die due to senescence, and "not by an external force".
Being killed has always been undesirable, but it has not mainly been what humans dreamed of avoiding. Escape from the inevitable death caused by old age, however, has been the subject of much of the fiction in human history. That there are many immortal Greek figures that are kill-able, but do not die of senescence, proves this.
When you want to talk about something fictitious, you decide what it means. So you can define immortality the way you want. So you may define your legendary creature as one that doesn't even die due to injuries etc. Or, you could take a look at nature.
The closest nature has to immortality is the doesn't-die-by-senescence version:
Biological immortality has gained recent interest among researchers. See also a question about Immortal organisms on biology.SE.
Bottom line is, you can. The implied meaning has usually been very close to what you think. Vampires have sometimes been absolute im-mortals, sometimes beheading killed them, and sometimes silver bullets.
Best Answer
Worship would be felt odd here, because it implies not only love but deep reverence. However, adore (which originally meant the same thing as worship) has mostly lost its religious sense and may be used to express extravagant affection.