How can someone get rid of material possessions that don't contribute much towards their values in life?

If the ‘fascination towards material objects’ leaves, the loss in spirituality also leaves!0

~ Param Pujya Dada Bhagwan

Spirituality is the most valuable thing. When one progresses in spirituality, one’s values in life are automatically enriched.

So, to answer your question, following are some of the quotes of Param Pujya Dada Bhagwan, which you can ponder upon; and it will lead you in the right direction.

Anything that one does in order to attain the Self (Atma) is spirituality. This is the main production, as a consequence of which, one automatically receives all worldly necessities as a by-product.
For worldly wealth, you have to go in one direction, and for spiritual wealth, you have to go in the other. So would it not hinder you if you were going in the wrong direction? Therefore, it becomes a complete obstacle in life. Spiritualism and materialism lie in opposite directions.
That which makes our mind and consciousness go astray and wild is all kusang (whose company takes us away from the Self — the pure Soul). That which pacifies the mind and consciousness is satsang (whose company takes us to the eternal truth).
Misery will not leave from where there’s excessive bad or harmful associations with that which takes you away from the Self (kusang). Whereas happiness will not leave from there where there’s excessive association with Self-realized beings or spiritual discourses (satsang)!
Until one is under societal influence (lok-sangnya), there is nothing but pain there, and if one comes under the influence (sangnya) of Gnani, the Enlightened One, then there is nothing but happiness, happiness, and even more happiness. What is lok-sangnya? Loksangnya means to believe that there is happiness in whatever people have believed there to be happiness in; say they have believed there to be happiness in materialistic things, you too believe the same. And to believe that there is happiness only in the Self (the Pure Soul) is the sangnya of the Gnani!
Has anyone truly become prosperous in this world? Everyone is after worldly prosperity, but has anyone ever really succeeded? Man does not have any authority over this. If nothing is under one’s authority, what is the point of all this useless restlessness? It is all meaningless!
Through the five senses and with the help of ego, intellect, mind, etc. we experience worldly things. This continues life after life, and lastly we find out that there is no permanent happiness in this material world; all the material happiness is temporary and material things also are temporary — they give only temporary happiness. This is when the person starts hunting for permanent happiness.
When one comes out from the lust for temporary things and realizes the eternal Soul, it marks the beginning of spirituality.
Inspite of experiencing immense pleasure, one is not contented. It is because this pleasure is not real pleasure. Real pleasure is that which once you experience, there will never be any pain following it thereafter. The experience of such pleasure in human birth is called moksha i.e. freedom from all forms of suffering. This is the first stage of moksha (liberation). The ultimate moksha happens when one’s all karma come to an end. But the first stage of moksha is possible here, in this life only, by attaining the Self.
God (the Absolute Self, Parmatma) is an abode of endless bliss!!! If you like happiness and you do not like misery, then worship God (the pure Soul residing within, Parmatma). And if you like misery and do not like happiness, then worship the material things.
For moksha, it is not the worldly life that gets in the way; it is the ignorance of the Self. The Gnani Purush gives you such a precise and unfailing knowledge of Self that it immediately comes into your experience. The knowledge that gives results is real knowledge!
Attraction towards material things throws us into the dangerous currents like that of whirlpool!

However, it is Gnani, in whose heart compassion incessantly flows, who throws the net, stops us from being drawn into these dangerous currents, and saves us from the miseries of infinite births!!!

Therefore, one must try and remain in the company of Gnani as much as one can. One will soon develop such attraction towards him which no material possessions shall be able to match. Then, one will readily throw away anything and everything that doesn’t contribute to your ultimate liberation.

And when one attains Self-Realization from this Gnani, one realizes that, ‘I am a pure Soul, whose inherent nature is permanent happiness (eternal bliss)!’; one tastes the permanent happiness. Thereafter, as one stays more and more in the awareness of Pure Soul, attraction or hatred towards any material possessions does not occur. Consequently, the Soul comes to a state where it is totally free of any kind of attachment towards the material possessions.

Thus, this is the easiest way around to get rid of whatever you feel is coming in your way to liberation!