I looked the at the use of 感じる a few months ago. I came to the following conclusions:
The verb is usually transitive (他動詞) ; it takes を with a noun (including embedded noun phrases with の）but
It can also be intransitive (自動詞): Space ALC list it as both and give the example ～が退屈に感じる (feel bored ［uninspired］).
It can also take と to mark a "quotation/sound or manner adverbial" phrase, in which case the と seems to follow a verb (and I think we can say 感じる here is intransitive).
- When it appears to take に, the に particle is actually marking an adverb. This happens with transitive and intransitive uses of the verb.
- It also communicates three different ways of "feeling".
I have tried to explain #5 below with carefully chosen examples of 1-4 which can be picked out with little difficulty:
I classify the three feelings as Physical, Emotional and "Spider" (because the last is somewhat intuitive, similar to the way that Spiderman can sense danger). Examples of each are as follows:
Physical sense (五感で刺激を受ける)：
家が揺れるのを感じた｜I felt the house shake.
Emotional sense (eg to be moved ｟by｠; be impressed ｟by｠):
その時，初めて母の愛を深く感じた｜I had never felt my mother's love so strongly.
Did you have some special reason of your own for giving up such a good job?
Spider-sense (eg to sense ｟that｠):
彼は生命の危険を感じた｜He sensed that his life was in danger.
彼ががっかりしているのを感じた｜I [was aware of / sensed] his disappointment.
彼は何かを隠していると感じた｜I felt that he was keeping something from me.
The follow-up question to this explanation might be what is the difference between expressions taking と and を？ Very briefly:
(i) Some verbs such as 思う always takes と (another example would be jumping to a conclusion, 早合点する）
(ii) Some verbs such as 忘れる and 思い出す never take と because you can only remember/forget facts not beliefs!
(iii) Some verbs such as 考える ＆ 分かる take both because they can take two meanings: You can either just think (ie believe) or think about something (ie consider facts), either is possible.
感じる falls under category (iii), as can be seen from the examples above.