هذا شعور غريب.

Word by word:

• هذا = this
• شعور = feeling
• غريب = strange / odd / unusual

So the sentence literally matches This [is] a strange feeling.

In Arabic, the present tense of to be is usually not stated in sentences like this.

So:

• هذا شعور غريب literally looks like this a strange feeling
• but it naturally means This is a strange feeling

This is very common in Arabic nominal sentences.
If you wanted a past tense meaning, then Arabic would use a verb, for example something like كان for was.

هذا is the demonstrative pronoun meaning this for a masculine singular noun.

Since شعور is a masculine singular noun, Arabic uses:

• هذا = this (masculine)
• not هذه = this (feminine)

So هذا شعور غريب is the correct choice for this is a strange feeling.

شعور is masculine in Modern Standard Arabic.

That matters because words that describe it must match it. So the adjective is:

• غريب = masculine singular

If the noun were feminine, the adjective would usually take a feminine form instead.

In Arabic, adjectives normally come after the noun they describe.

So:

• شعور غريب = a strange feeling
• literally: feeling strange

This is the normal Arabic order:

• noun + adjective

Also, the adjective agrees with the noun in:

• gender
• number
• definiteness
• case

So غريب matches شعور.

They are indefinite because the meaning is a strange feeling, not the strange feeling.

So:

• شعور غريب = a strange feeling
• الشعور الغريب = the strange feeling

In Arabic, adjective phrases match in definiteness too:

• indefinite noun + indefinite adjective
  شعور غريب
• definite noun + definite adjective
  الشعور الغريب

That is why there is no ال on either word in your sentence.

They are similar, but not identical.

• هذا شعور غريب = This is a strange feeling
• هذا الشعور غريب = This feeling is strange

In the first sentence, شعور غريب is an indefinite phrase: a strange feeling.
In the second, الشعور is definite: the feeling / this feeling, and غريب is the predicate adjective: strange.

So the difference is mainly about whether you are introducing a feeling or talking about a specific feeling.

Yes. It is a complete nominal sentence.

A simple way to understand its structure is:

• هذا = the topic / subject-like element
• شعور غريب = the information being given about it

In traditional grammar terms, Arabic often analyzes this kind of sentence as a nominal sentence with a subject and predicate.

So even without a verb, it is fully complete and natural.

A careful MSA pronunciation is approximately:

hādhā shuʿūrun gharībun

A few notes:

• هذا = hādhā
• شعور = shuʿūr
• غريب = gharīb

In normal pausal pronunciation, the final case endings are often not pronounced, so you will often hear:

hādhā shuʿūr gharīb

Also:

• ع in شعور is a consonant that does not exist in English
• غ in غريب is a voiced guttural sound, somewhat like a French r to many learners

In full formal Arabic, both شعور and غريب are in the nominative, so they can take -un when indefinite:

• شعورٌ
• غريبٌ

So the fully inflected form is:

هذا شعورٌ غريبٌ

Why nominative? Because in this kind of nominal sentence, the predicate part is nominative in standard grammar.

In everyday reading and speech, these short vowel endings are often omitted in writing and often not pronounced in pause, which is why you commonly see:

هذا شعور غريب

Sometimes, yes, depending on context. But feeling is the most direct and natural choice here.

شعور can refer to:

• feeling
• sensation
• sense
• emotion, in some contexts

In هذا شعور غريب, feeling is usually the best translation because it sounds natural in English and fits the sentence well.