You are right that those verses appear quite shocking on simple reading. However, they are much more understandable based on the interpretations of the Sages.

Before beginning, I will note that according to the Sages the subjects of the two verses are somewhat different. We will therefore explain each one separately below.

Verse 28 reads as follows:

However, any doomed item which a man dooms to God of anything that is his, whether a person, animal, or the field of his heritage, may not be sold and may not be redeemed. All doomed items are holy of holies to God.

There is some debate in the Talmud (Erchin 28-29) regarding the precise meaning of the verse, but the principles are fairly well agreed upon. We can “doom” objects to God either by consecrating them to the Temple or to the Priests. When we do so, they become Temple or Priestly property. We may only consecrate that which belongs to us – whether our land, house, movables, animals or slaves. (This is the intent of the “person” mentioned in the verse; Talmud Gittin 38b, Erchin 28b.)

What does the Temple do with property consecrated to it? An animal fit for a sacrifice will be offered to God. Anything else will generally be sold by the Temple treasurers and the proceeds will go to the Temple treasury. (The owner himself can redeem what he consecrated by adding 25% to its appraised value.) All of the above is basically the subject of Leviticus 27.

Verse 28 discusses items consecrated to the Priests. Such items may not be sold by the Temple custodians and may not be redeemed by the donor (“may not be sold and may not be redeemed”). Rather, they become permanent Priestly property, divided up among the Priestly family on duty at the time the gift is dedicated. (Once the Priests divide them, they have no sanctity and can be used for ordinary household use (Talmud Erchin 29a).)

(The final phrase of the verse appears to refer to items consecrated to the Temple – which so become “holy of holies.” The precise interpretation is discussed by the Talmud (Erchin 28-29).)

Verse 29 is unrelated. It reads as follows:

Any doomed item which has been banned from mankind shall not be redeemed. It shall surely be put to death.

What is the meaning of this cryptic, ominous verse? There are two opinions (both appearing in Talmud Erchin 6b):

(1) The “doomed item” of the verse refers to a person (the Hebrew gives no indication if a person or object is intended). The “doomed” person is one whom the courts have condemned to death – and as a result, is banned from mankind. If a person vows to donate his worth to the Temple (see e.g .Leviticus 27:2-7) he owes nothing. Since the person is about to be killed he has no “worth”.

(2) As above, the “doomed item” is a person condemned to death. He may not “redeem” himself by paying money to commute his sentence, but rather he must be put to death.

(Regarding Jephthah, although almost all the commentators do not understand that he literally killed his daughter (see this past response), there is one interpretation that he did. The commentator Ramban (Nachmanides) explains that Jephthah erred in his interpretation of this verse, thinking that the law that a doomed person must be put to death extends even to decrees made by a ruler and even though his daughter did no wrong.)