Assalaamu alaykum. My question is the following: for example, I stay with people that are not really worried about eating stolen foods or using stolen perfumes and so on. If I get into contact with those foods, perfumes, and so on, can I then pray in this state, or do I have to wash it off? Please note that it is really hard to avoid.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.

There is no doubt that theft is prohibited in Islam and that the stolen item must be returned to the rightful owner.  However, the stolen item is not considered impure in and of itself. Accordingly, if the stolen item is ritually pure, be it food or perfumes, then you are not obliged to wash whatever body part or clothes touched it. If you doubt the ritual purity of the stolen item, then you should know that the basic principle in this case is that all things are ritually pure unless proven otherwise. Skaykh Ibn Taymiyyah wrote, "The prescribed thing to be done in this case is to apply the principle of istis-haab (i.e. presumption of the existence or non-existence of a fact that is proven in the past and is presumed to remain as so in the future until it is proven through evidence). If there is evidence indicating the impurity of such an item, then it is declared impure; otherwise, it is not recommended to avoid using it merely based on the possibility of being impure..." [Majmooʻ Al-Fataawa]

If the people with whom you are staying commit theft, then you should advise them and remind them of the prohibition of what they are doing. If they continue to commit this sin, then you should find another place to stay, if possible. Verily, the company of wicked people brings about nothing but evil. The Prophet likened the wicked and evil friends to the iron-smith blowing a pair of bellows; he will either burn your clothes or, at least, you will perceive a bad scent from him.

Abu Moosa narrated that the Prophet said, "The example of a good companion and an evil one is that of the seller of musk and the blower of the bellows (iron-smith). The seller of musk will either give you some of the musk, or you will purchase some from him, or at least you will enjoy its good smell, whereas the blower of the bellows will either burn your clothing or, at least, you will suffer its repugnant smell." [Al-Bukhari and Muslim]

An-Nawawi commented on the hadith, saying:

"In this hadith the Prophet likened a good companion to the one who carries musk and the bad companion to the iron-smith blowing a pair of bellows. It points out the merits and virtue of keeping the company of righteous, noble, ethical people who are endowed with mindfulness of Allaah, knowledge, and refined manners. It also indicates that it is not allowed to keep the company of wicked, evil people and followers of religious innovations, those who backbite people or those who are idle and foul-mouthed, and others known for blameworthy acts and traits." [Sharh Muslim]

Allaah knows best.